Do your college not want you to do the rest because of your mental health? Or because you have missed the first two exams? I think you need to speak to them, it's no good them saying you might not be able to - you need to know one way or the other. However if the impact on your mental health is too much then it would be better if you didn't do them. Further maths is supposed to be a ******* of a course that a a lot of people drop out of - is it strictly necessary for what you want to do? Are you putting way too much pressure on yourself to do it when you don't absolutely have to? Have you been able to sit your other exams? There is so much more to life than exams, especially further maths and anything causing you this much stress and anxiety just isn't worth it.
If school/college says they withdrew you due to anxiety (you don't have to be suicidal) then it can go on your other results. I don't know exactly the rules or how many you do have to sit I only know that someone didn't do one of their GCSE papers due to very bad anxiety at my school and they got their grade based on the exams they did.
I would look at the bigger picture though, do you really need FM? Do you have 3 other A-levels? A lot of schools only allow FM as a 4th subject because the drop out rate is so high. Could you find a different route to do what you want? Can you do a foundation year at uni if that's where you want to go. Honestly the thing you need to worry about and concentrate on is your mental health and it sounds like you're really struggling. Get as much support and help as you can - do you have any access arrangements in place for exams? You sound very vulnerable so I think they should be providing you with a small room and rest breaks. Go speak to the exams officer at college, say you need a definite answer and take it from there - but put your mental health first. Nothing is worth more than that.