Metal organic frameworks (MOFs) are great candidates for capturing 02 due to their highly porous structures and tunable physical and chemical properties. In this study, we assessed the performance of 1525 biocompatible MOFs which have endogenous linkers and nontoxic metal centers for adsorption-based and membrane-based O-2 separation and also for high-pressure O-2 storage. We initially computed Henry's constants of O-2 and N-2 at zero coverage and 298 K by performing Grand Canonical Monte Carlo (GCMC) simulations and estimated infinite dilution adsorption selectivities for O-2/N-2 mixture. We performed binary mixture GCMC simulations for the top 15 candidates at various pressures and 298 K and compared mixture adsorption selectivities with those obtained from infinite dilution. We then estimated O-2 working capacities of 315 biocompatible MOFs obtained at 298 K and 140 bar for storage and 5 bar for release pressures. Our results showed that 15 biocompatible MOFs outperform gravimetric O-2 working capacities of the traditional adsorbent materials such as activated carbon and NaX and some common MOFs such as NU-125 and UMCM-152 at 298 K. We finally calculated O-2 and N-2 permeabilities and membrane selectivities of 45 promising MOF candidates for O-2/N-2 separation. Seventeen biocompatible MOF membranes were identified to exceed the Robeson's upper bound established for polymers. This computational study will be useful to identify the promising biocompatible MOFs for storage and separation of O-2. The bio-MOF library constructed in this study will also guide both experimental and computational studies for design and development of biocompatible MOFs for various medical applications.