Venetoclax and Acalabrutinib in Treating Patients With Relapsed or Refractory Mantle Cell Lymphoma

Inclusion Criteria: * Confirmed diagnosis of MCL in previously treated relapsed/refractory patients with/without chromosome translocation t(11;14), (q13;q32) by FISH and/or overexpress cyclin D1 in tissue biopsy (blastoid/pleomorphic morphology, complex karyotype is acceptable), cyclin D1 negative mantle cell lymphoma is allowed. MCL diagnosis confirmation is needed by pathologist. * Disease had relapsed after or been refractory to \>= 1 prior therapy for MCL and now requires further treatment. * Ability to understand the purpose and risks of the study and provide signed and dated Institutional Review Board (IRB) approved informed consent and authorization to use protected health information (in accordance with national and local patient privacy regulations). * Willing and able to participate in all required evaluations and procedures in this study protocol, including swallowing capsules and tablets without difficulty. * Age ≥ 18 years at the time of signing the ICF. * Bi-dimensional measurable disease using the Cheson criteria (measurable disease by computed tomography \[CT\] scan defined as at least 1 lesion that measures \>= 1.5 cm in single dimension). Gastrointestinal (GI), bone marrow or spleen only patients are allowable. * Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2 with no deterioration over the previous 2 weeks prior to baseline or day of first dosing. The following laboratory criteria must be met * Absolute neutrophil count (ANC) \> 1,000/mm\^3 independent of growth factor support. * Platelet count \>= 100,000/mm\^3 or \>= 50,000/mm\^3 if bone marrow involved with lymphoma, independent of transfusion support in either situation. * Creatinine (Cr) =\< 2 or Cr clearance \>= 30 mL/min. * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \< 3 x upper limit of normal (ULN), serum bilirubin \< 1.5 mg/dl, unless due to Gilbert's syndrome, documented liver involvement with lymphoma, or of non-hepatic origin. * Prothrombin time (PT)/international normalized ratio (INR) =\< 1.5 x ULN and partial thromboplastin time (PTT) =\< 1.5 x ULN. * Disease free of prior malignancies other than MCL with exception of currently treated basal cell, squamous cell carcinoma of the skin, carcinoma "in situ" of the cervix or breast, or other malignancies in remission (including prostate cancer patients in remission from radiation therapy, surgery or brachytherapy), not actively being treated with life expectancy of \> 3 years. Principal investigator (PI) can use clinical judgement in the best interest of patients. * Females of childbearing potential (FCBP) must have a negative serum or urine pregnancy test and willing to use highly effective methods of birth control. * Male subjects must agree to refrain from sperm donation during the study. * A female of childbearing potential is a sexually mature woman who: * Has not undergone a hysterectomy or bilateral oophorectomy; or * Has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months). Exclusion Criteria: * Prior treatment with acalabrutinib or any investigational drug within 30 days or 5 half-lives (whichever is shorter) before first dose of study drug. * History of prior malignancy that could affect compliance with the protocol or interpretation of results, except for the following: 1. Curatively treated basal cell carcinoma or squamous cell carcinoma of the skin or carcinoma in situ of the cervix or carcinoma in situ of the prostate at any time prior to study. 2. Other cancers not specified above that have been curatively treated by surgery and/or radiation therapy from which subject is disease-free for ≥3 years without further treatment. * Any serious medical condition including but not limited to, uncontrolled hypertension, uncontrolled diabetes mellitus, active/symptomatic coronary artery disease, chronic obstructive pulmonary disease, renal failure, active hemorrhage, or psychiatric illness that, in the investigator's opinion places the patient at unacceptable risk and would prevent the subject from signing the ICF. * Pregnant or breast-feeding females. * Known human immunodeficiency virus (HIV) infection. * Uncontrolled autoimmune hemolytic anemia (AIHA) or idiopathic thrombocytopenic purpura (ITP). History of or ongoing confirmed progressive multifocal leukoencephalopathy (PML) * Any active significant infection (e.g., bacterial, viral or fungal, including subjects with positive cytomegalovirus \[CMV\] DNA polymerase chain reaction \[PCR\]). * Serologic status reflecting active hepatitis B or C infection. * a. Subjects who are hepatitis B core antibody (anti-HBc) positive and who are hepatitis B surface antigen (HBsAg) negative will need to have a negative PCR result before randomization and must be willing to undergo DNA PCR testing during the study. Those who are HbsAg-positive or hepatitis B PCR positive will be excluded. b. Subjects who are hepatitis C antibody positive will need to have a negative PCR result before randomization. Those who are hepatitis C PCR positive will be excluded. * Central nervous system (CNS) disease with serious significance. * Refractory nausea and vomiting, inability to swallow the formulated product, or Malabsorption syndrome, disease significantly affecting GI function, or resection of the stomach or small bowel or ulcerative colitis, symptomatic inflammatory bowel disease, or partial or complete bowel obstruction, or any other GI condition that could interfere with the absorption metabolism, and excretion of acalabrutinib or venetoclax. * Major surgical procedure within 30 days before the first dose of study drug. Note: If a subject had major surgery, they must have recovered adequately from any toxicity and/or complications from the intervention before the first dose of study drug. * Known bleeding diathesis (e.g., von Willebrand's disease) or hemophilia. * History of stroke or intracranial hemorrhage within 6 months prior to study entry * Requires anticoagulation with warfarin or equivalent vitamin K antagonist * Vaccinated with live, attenuated vaccines within 4 weeks of study entry * Concurrent systemic immunosuppressant therapy (e.g., cyclosporine, tacrolimus, etc., or chronic administration of \>10mg/day of prednisone or equivalent) within 28 days of the first dose of study drug. * Requires treatment with strong CYP3A inhibitors or inducers or strong CYP1A2 inhibitors (refer to list in Appendix V and Sections 8.2.1 and 8.2.2). * Refractory to prior ibrutinib or BTK mutation or previous exposure to other BTK inhibitors