I agree with quiltsRfun - the ironing board is probably the problem. I've used my rotary cutter on the ironing board, and it was awful. The mat really needs to be on a solid, flat surface. If you really don't have anywhere else to cut (kitchen table? island/peninsula?), then maybe get a pre-fab shelf from Home Depot, as long as it's at least as big as your cutting mat. Place the shelf on top of the ironing board but under the mat; it will still probably squish a little, but it will be miles better than the mat directly on the ironing board surface.
I have the same Fiskars rotary cutter as you, and like it, but I know some people that find that handle style very uncomfortable. Try going to a craft store and holding a few different ones, and seeing if there is a style that feels better in your hand.
Good luck!