"to cut my hair"--normal, common. "to cut off my hair"--unusual. To remove most or all of one's hair. "to chop off my hair"--unusual. Suggests a very bad, careless haircut. "When I was younger, to save money, my wife cut my hair." "I'm going to get my hair cut." "I'm need to get a haircut [noun, one word]." All natural, common, normal things to say. To "cut OFF my hair" suggests cutting most or all of it off. It is not a normal thing: "I got glue in my hair! It was so bad that I needed to cut off most of my hair!" You "cut" with scissors. You "chop" with an axe. To "chop my hair off" means to cut badly and quickly. "I got a very bad haircut. He didn't cut my hair, he just chopped it off."

'Chop' suggests a crude and violent movement, like chopping down a tree with an axe. For example, 'She was so angry and frustrated that she took a kitchen knife and chopped off all her hair'. 'Cut' is a neutral term. We don't know how it is done, or how much is cut off. 'Cut off' sounds much more radical. As I'm sure you know, adding 'off' to a verb makes the action stronger, more complete and more definitive. If you say 'I'm going to cut my hair ', it might just be a trim. If you say 'I'm going to cut my hair off', you'd imagine someone with a very long hair who is planning to make a dramatic change.