Cut the caulk in the joint between the baseboard tiles and the floor into 1-foot-long strips, using the edge of a putty knife. Dig the cut strips of caulk out of the joint with the corner of the knife, exposing the joint completely. Repeat the process for the caulked line along the top of the tiles.
Remove the grout between the joints of the baseboard tiles using a carbide grout blade attached to a rotary tool. Allow the blade to spin at full speed before touching it to the grout, and cut the grout slowly, opening the joint between the tiles to the level of the adhesive beneath.
Slip a pry bar between the top of the tile and the wall, unless that angle is blocked by fixtures. Wiggle the end of the bar slightly as you press it beneath the tile in order to wedge the tile slightly away from the wall. The adhesive bond holding the tile into place should begin to fail. Apply pressure with the pry bar against the rear of the tile, forcing the tile away from the wall until it pops free.