Inclusion Criteria:
* Documented informed consent of the participant and/or legally authorized representative.
* Assent, when appropriate, will be obtained per institutional guidelines
* Agreement to allow the use of archival tissue from diagnostic tumor biopsies
* If unavailable, exceptions may be granted with study principal investigator (PI) approval
* Age: ≥ 18 years
* Eastern Cooperative Oncology Group (ECOG) ≤ 2
* Histologically or flow cytometry confirmed diagnosis of B-CLL/SLL as documented by medical records and with histology based on criteria established by the World Health Organization (WHO)
* No prior treatment for CLL/SLL, except steroids and/or rituximab to treat autoimmune complications
* Active disease meeting criteria for requiring treatment per the International Workshop on Chronic Lymphocytic Leukemia (iwCLL) 2018 guidelines
* A minimum of any one of the following constitutional symptoms:
* Unintentional weight loss \> 10% within the previous 6 months prior to screening.
* Extreme fatigue (unable to work or perform usual activities).
* Fevers of greater than 100.5°F for ≥ 2 weeks without evidence of infection.
* Night sweats without evidence of infection.
* Evidence of progressive marrow failure as manifested by the development of, or worsening of anemia or thrombocytopenia.
* Massive (i.e., \> 6 cm below the left costal margin), progressive or symptomatic splenomegaly.
* Massive nodes or clusters (i.e., \> 10 cm in longest diameter) or progressive lymphadenopathy.
* Progressive lymphocytosis with an increase of \> 50% over a 2-month period, or an anticipated doubling time of less than 6 months.
* Autoimmune anemia or thrombocytopenia that is poorly responsive to corticosteroids.
* Symptomatic or functional extranodal involvement (eg, skin, kidney, lung, spine)
* Participant must be able to swallow tablets or capsules. A participant with any gastrointestinal disease that would impair ability to swallow, retain, or absorb drug is not eligible
* Absolute neutrophil count (ANC) ≥ 500/mm\^3
* Platelets ≥ 30,000/mm\^3
* Total bilirubin ≤ 2 X upper limit of normal (ULN) (unless has Gilbert's disease or compensated hemolysis directly attributable to CLL)
* Aspartate aminotransferase (AST) ≤ 2.5 x ULN
* Alanine aminotransferase ≤ 2.5 x ULN
* Creatinine clearance of ≥ 30 mL/min per 24 hour urine test or the Cockcroft-Gault formula
* If not receiving anticoagulants: International Normalized Ratio (INR) OR Prothrombin (PT) ≤ 1.5 x ULN. If on anticoagulant therapy: PT must be within therapeutic range of intended use of anticoagulants
* If not receiving anticoagulants: Activated Partial Thromboplastin Time (aPTT) ≤ 1.5 x ULN. If on anticoagulant therapy: aPTT must be within therapeutic range of intended use of anticoagulants
* If seropositive for HIV, hepatitis C virus (HCV) or hepatitis B virus (HBV), nucleic acid quantitation must be performed. Viral load must be undetectable. HIV-infected patients on active anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial
* Women of childbearing potential (WOCBP): negative urine or serum pregnancy test. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required
* Agreement by females and males of childbearing potential\* to use an effective method of birth control or abstain from heterosexual activity for the course of the study and after completion of study treatment as described below separately for males and females.
* Female participants must remain abstinent or use contraceptive methods with a failure rate of \< 1% per year during the treatment period and for at least 2 days after the final dose of acalabrutinib, 30 days after the last dose of venetoclax, and 3 months after the final dose of tafasitamab, whichever is longer. Women must refrain from donating eggs during this same period.
* Examples of contraceptive methods with a failure rate of \< 1% per year include bilateral tubal ligation, male sterilization, hormonal contraceptives that inhibit ovulation, hormone-releasing intrauterine devices, and copper intrauterine devices.
* Hormonal contraceptive methods must be supplemented by a barrier method.
* For male participants: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods, and agree to refrain from donating sperm, as defined below:
* With a female partner of childbearing potential or pregnant female partners, male participants must remain abstinent or use a condom plus an additional contraceptive method that together result in a failure rate of \< 1% per year during the treatment period and for at least 2 days after the final dose of acalabrutinib, 90 days after the last dose of venetoclax, and 3 months after the final dose of tafasitamab, whichever is longer. Male participants must refrain from donating sperm during this same period.
* The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the individual. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not adequate methods of contraception.
* A woman is considered of childbearing potential, ie, fertile, following menarche and until becoming postmenopausal unless permanently sterile. Permanent sterilization methods include hysterectomy, bilateral salpingectomy, and bilateral oophorectomy. Contraception methods include the following:
* Combined (estrogen- and progestogen- containing) hormonal contraception associated with the inhibition of ovulation
* Oral, intravaginal, or transdermal
* Progestogen-only hormonal contraception associated with the inhibition of ovulation
* Oral, injectable, implantable
* An intrauterine device
* Intrauterine hormone-releasing system
* Bilateral tubal occlusion Vasectomized partner (provided that the vasectomized partner is the sole sexual partner of the woman of childbearing potential study participant and that the vasectomized partner has received medical assessment of surgical success)
* Sexual abstinence (defined as refraining from heterosexual intercourse during the entire period of risk associated with the study treatment, starting the day prior to first dose of study drug, for the duration of the study, and for ≥ 90 days after the last dose of zanubrutinib or ibrutinib. Total sexual abstinence should only be used as a contraceptive method if it is in line with the patients' usual and preferred lifestyle. Of note, barrier contraception (including male and female condoms with or without spermicide) is not considered a highly effective method of contraception, and, if used, this method must be used in combination with another acceptable method listed above. If patient is using hormonal contraceptives such as birth control pills or devices, a barrier method of contraception (eg, condoms) must also be used. A postmenopausal state is defined as no menses for 12 months without an alternative medical cause. A high follicle-stimulating hormone level in the postmenopausal range may be used to confirm a postmenopausal state in women not using hormonal contraception or hormonal replacement therapy. However, in the absence of 12 months of amenorrhea, a single follicle-stimulating hormone measurement is insufficient
Exclusion Criteria:
* Chronic use of corticosteroids in excess of 20 mg/day prednisone or its equivalent
* Major surgery (under general anesthesia) within 30 days prior to therapy
* Uncontrolled coagulopathy or bleeding disorder. Direct oral anticoagulants are allowed
* Use of moderate or strong cytochrome P450 3A4 (CYP3A4) inducer within 2 weeks of the first day of study therapy. CYP3A inhibitors are allowed
* Exposure to vaccination with live vaccine within 30 days prior to cycle (C) 1 day (D) 1, or anticipated need for such vaccination during treatment
* History of prior malignancy except:
* Malignancy treated with curative intent and no known active disease present for ≥ 2 years prior to initiation of therapy on current study;
* Adequately treated non-melanoma skin cancer or lentigo maligna (melanoma in situ) without evidence of disease
* Adequately treated in situ carcinomas (e.g., cervical, esophageal, etc.) without evidence of disease;
* Asymptomatic prostate cancer managed with "watch and wait" strategy;
* Uncontrolled immune hemolysis or thrombocytopenia (positive direct antiglobulin test in absence of hemolysis or history of immune-mediated cytopenias are not exclusions)
* Active infection
* Known positive test result for hepatitis C (HCV antibody serology testing) and a positive test result for HCV ribonucleic acid (RNA). Participants with positive serology are eligible in case of negative HCV RNA test results
* Known active hepatitis B virus (HBV) or hepatitis C virus (HCV) infection. Patients with past HBV infection (defined as negative hepatitis B surface antigen (HBsAg) and positive hepatitis B core antibody \[HBcAb\]) are eligible if HBV deoxyribonucleic acid (DNA) is undetectable. Patients who are positive for HCV antibody are eligible if polymerase chain reaction (PCR) is negative for HCV RNA
* Known active human immunodeficiency virus (HIV) infection. Subjects who have an undetectable or unquantifiable HIV viral load with CD4 \> 200 and are on highly active antiretroviral therapy (HAART) medication are allowed. Testing to be done only in patients suspected of having infections or exposures
* Females only: Pregnant or breastfeeding
* Any other condition that would, in the Investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures
* Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)