I learned years ago in Scouts that to get a tick to let go, strike a match, and while the matchhead is hot, blow it out and immediately touch it to the tick. It'll let go so you can remove it head and all. I've never had to put that into practice, but here's a site (among several) that confirms how to do it.
Women Anglers, Melanie Calvert-Benton, Tick Borne Diseases