Tumor mutation profiling (MP) is often conducted on tissue from biopsies conducted for clinical purposes (diagnostic tissue). We aimed to explore the views of patients with cancer on who should own tumor biopsy tissue, pay for its storage, and decide on its future use; and determine their attitudes to and predictors of undergoing additional biopsies if required for research purposes. In this mixed methods, cross-sectional study, patients with advanced solid cancers enrolled in the Molecular Screening and Therapeutics Program (n = 397) completed a questionnaire prior to undergoing MP (n = 356/397). A subset (n = 23) also completed a qualitative interview. Fifty percent of participants believed they and/or relatives should own and control access to diagnostic tissue. Most (65.5%) believed the government should pay for tissue preparation. Qualitative themes included (1) custodianship of diagnostic tissue, (2) changing value of tissue across time and between cultures, (3) equity regarding payment, and (4) cost-benefit considerations in deciding on additional biopsies. Policy and regulation should consider patient perspectives. Extension of publicly funded health care to include tissue retrieval for clinical trials should be considered.