How can I remove tiles without damaging the heating mat underneath?
I assume you will put new tiles on top of the heating pad. It is very tedious to remove tiles without damaging the heating pad. I would do it using hand tools (hammer, chisels) or low powered tools (dremel). I would cut out the grout lines first and start chipping the tiles.  It goes without saying this is very time consuming if you have a large area (usually kitchens are).

But once the tiles are off, cleaning up the thinset left on your mat is even more challenging.  There are much more chances of damaging the mat in this step and no good way to remove it. Typically I remove the thinset with a grinder using a concrete disk. But doing it while avoiding contact with the mat seems difficult and stressing to me. The grinder can be rather unforgiven and we need to keep it steady over a long period of time. The heating mat is also not completely flat (usually look like below).  You need to clean the floor well for the new thinset to achieve a good bond with your floor.

The solution comes down to time vs cost.  I would personally replace the mats if they are old.  You will save time and money.  New mats are more energy efficient.