Due to my depression, the department wants to kick me out of the graduate program. How to stay in this environment?
I'm having some trouble with the way you're mixing the words trouble, troubled and troubling.

If a student shows some red flags for possible suicidal thoughts, it's a good thing when the people around him alert the department, in order for support to be offered.

On the other hand, targeting the troubled student and painting him as a troublemaker would not be good.

As you are currently not in as good shape, mental health-wise, as you would like, it's difficult for me to know how objectively you are able to be, currently, in your perceptions and interpretations.  That is, I'm not sure whether your colleagues are actually targeting you for possible removal from your academic program.

However, I will go ahead and do my best to answer.  I'm not sure what country you're in, or what the laws and regulations are where you are, so I'll write the answer I would give to someone facing the problems you described in the U.S.

People fear what they don't understand.  The key to acceptance of a mental health disability is education -- both of staff and peers.

In the U.S., I would ask NAMI, the National Alliance on Mental Illness, or a local disability rights group, or a county mental health association, to send a trained expert to give a mental health awareness presentation to the students, and a separate training session for staff.

Here is an example of a presentation that a college student gave about her neurological disability, Tourette Syndrome, to her classmates, with the help of a staff ally: https://youtu.be/zVY6B3ezY3k

I get the feeling from your post that you might not be in the right place at this time to give a presentation of this type yourself.  That's okay.  There are people who have experience giving presentations on behalf of a student.

Here is a nice website with suggestions for how to seek reasonable accommodations for a disability in the workplace (in the U.S.) -- I think this may give you some good ideas, and in general instill you with more of a belief that you are entitled to accommodations! -- Job Accommodation Network.

It would be great if you could participate in a peer to peer support group.  In the U.S., in order to find such a group, one can try to find such a group with the following techniques:


google
ask a mental health professional, since these providers often have an email discussion group through which they can query each other about such opportunities
ask a government information service (one reaches it by dialing 211)
ask a psychiatric ward at a local hospital
the campus counseling center may have organized some groups of this type
ask the county mental health association
ask NAMI
if necessary, take the initiative and form such a group