Flooring Tile - Enlarge hole in ceramic tile countertop

I am replacing a cooktop in a ceramic tile countertop and need to make the hole about 1 inch wider. I have been able to work some of the 4-inch tiles loose from the mortar bed. I need advice before making a mess out of this. If I am able to get the rest of the tiles loose, does it make sense that I could cut an inch off the inch-thick mortar base with wood backing using a carbide blade in a reciprocating saw? Then I could cut an inch off the tiles and replace them. Am I setting myself up for a disaster?

You could just cut through the whole thing togther with an angle grinder with a 4" dry diamond blade. Then use your sawzall with a wood blade to cut throut the plywood. THe angle grinder would be much easier to work through the mortar bed, have some one hold a shop vac along your cut line while you work. If you don't have an angle grinder, you could jsut rent one for the project or use it as an excuse to buy a new toy.