The first thing I would like to say is that I hope you are okay. Be careful and definitely try to get to your uni's mental health care center if you feel that's a viable option. Maybe even discuss the problem with them :/ It's not a stupid reason...for those of us who've been suicidal in the past, even if we recover, it's very easy to slip back into those thoughts. It's like recovered alcoholics....even though they're clean, it's very easy for stressful or painful circumstances to drive them back into drinking, you know? :/
It's not stupid at all to think this way, feel this way, or react this way. Especially if you've been in that "swinging between happy and suicidal" place recently. It's very hard to not feel even more suicidal when under a lot of stress or when taken advantage of, which is almost definitely what's happening here.
That said, I would like to add that you should still have a lawyer or counselor or someone with law experience...maybe even a law professor at your school....look at this and determine if it's honestly something that's legally binding, and even if it is, maybe ask the professor if they would really sue you over this. Has he actually threatened legal action? That's very upsetting and kind of messed up.
It's unusual for a club to demand that you pay for a trip you sign up for even if you don't end up going. It sounds to me like this professor's trying to take advantage of you. I would encourage you to have someone with experience in law and maybe a department head or administrative faculty look at it and determine how binding it is. If all else fails, maybe even talk to the professor and flat out say "I do not have $750 to give you. I am sorry, but I do not possess the money. Even if you sue me, I will not have the money. In fact, if you sue me, I will have even less to give you. I am sorry, but I cannot pay you this. I did not know this was the case when I signed the contract." A lot of schools have policies for mediation between students and faculty in case of disputes; it's often in the student handbook. See if you can take advantage of those policies; if others can mediate for you, maybe you can get this dropped without the professor taking your money.
Even if it's not possible, see if you could maybe work out a payment plan. Unless this professor's just a real......unpleasant person....that might be a possibility.
I'm so sorry if you've already done this and it's hopeless :/ I just wanted to help. I'm so sorry you're going through this. :/