I posted this earlier but it seems to have got lost in the wires ...
I would drill a series of holes on the perimeter and then break-out (or cut-out, using a multi-tool) the centre piece. Doing the whole job with a multitool would take a while and make lots of fine dust (wear a mask!), and the vibration may loosen other tiles. A thought: is it possible to cut through the grout (multitool) and remove a tile to cut on the bench and then replace?