Sorry ... been there and hated that ... Try removing an entire floor of grout with a grout "removal tool", aka a grout saw. You will die!
I have removed grout using a 4 1/2" angle grinder and a masonry blade. It will rip throught the floor in no time. Use that tedious grout saw for tight spaces where the disk blade cannot reach.
Once you are done, use a shop vac to pick up the dust and fragments. Go about regrouting per usual.
You will be glad you used the grinder ...