The atomic structures, glass forming evolutions, mechanical properties and high pressure behavior of Mg75Zn20Ca5 and Mg60Zn35Ca5 bulk metallic glasses, which are promising candidates for biomedical implants, have been examined by using ab initio molecular dynamics simulations. The pair-distribution function and coordination number analyses show that increasing Zn content in the alloy results in a decrease in several bond distances and an increase in the total coordination number of each species due to the atomic size difference between Mg and Zn atoms. According to the Voronoi tessellation, bond pair and bond angle distribution analyzes, the fivefold geometrical arrangements (pentagonal-bipyramid) are the most predominant in the first coordination shell, indicating the stability of the amorphous states and their dense atomic packing. The most striking result emerged from the calculations of mechanical properties is that an increase of Zn (>= 30%) content in the alloy yields embrittlement in the alloys. Under uniaxial compressions, both compositions undergo structural failure between 6 and 8 GPa. Under hydrostatic pressure, a diminishing in fcc/hcp ordering and an enlargement of the ideal icosahedral ordering may indicate a more disordered structure. In our view, these results represent a good step toward understanding the atomic structures Mg-Zn-Ca bulk metallic glasses.