Good Morning Bec, and a warm welcome to you.
This isn't your fault and I agree with Tim when he says does 'she sees your moving out as a significant loss' and with MsPurple when she says 'Mental illness is never caused by one person or thing' and your mother can't try and stop you from going to uni by saying these awful comments.
Your mother needs medical help for her depression and anxiety and can't blame you for doing what you want to do and that's going to uni, and that her depression won't go away just by avoiding the situation that you have your own life to live.
Sometimes people make threatening comments to someone they love because they feel they will be lonely but need to understand that it's impossible to hold onto the only person they feel they have left.
It was sad when my 2 sons left home but I couldn't expect them to stay with me their whole life, they had their own ventures to pursue, but we are still in contact with each other.
Please look after your own health and if you feel as though you are beginning to feel a bit down, then please have a talk with the uni counsellor as well as your doctor.