It will be fine. You don' t want to do it more than once or twice though.

Our elk last year we cut it into cubes and froze the cubes until we had the time to rent a meat grinder to make hamburger (about 4 months later). We thawed it and ground it up. It was perfectly fine.

Also, the meat that grocery stores gets was frozen as sides of beef or pork before they get them and cut them up or grind it up. Do you think that meat would last as long as it would take to get it from the slaughter house, to the processing facility, to the distributers, to the stores if it wasn' t frozen before being cut into stakes and ground into burger? I doubt it.