Nearly all hardy geraniums (can't think of any right off that can't) can be cut back hard after the initial bloom sequence. In fact, most appreciate it by responding rapidly with a new flush of tidy foliage and often, additional flowering. Mowing is a less refined method of approaching this same process, but there's no reason why it shouldn't work, if you don't mind a somewhat chewed up appearance initially. The ones that would be less inclined to appreciate this treatment are the sprawling, rambling selections like 'Ann Folkard' or 'Rozanne'. So you are really not too limited by species or hybrid if you attempt this.

Gardengal, thanks so much! I have been trying for weeks to get back to this forum and I guess the link was broken. I just tried this morning and it didn't work but I was able to get to it by searching. Frustrating!!!