If I have a garnishmnet against me and am on my mothers account can they garnish her SS check? That is the only money deposited on that account

First its not a good idea to piggyback your question on someone else's. This can lead to confusion. You should start a new thread. So I've moved your question to its own thread.

Second, they can ATTACH (not garnish) any asset you are listed as part owner of. It would then be up to you to prove that all deposits into that account where your mom's and from exempt income. You MAY be able to head this off by giving the bank a letter stating that all the income is exempt. But the better option would be to remove yourself as Joint Tenant and just be authorized signator.

Yes they can until you can get their attention that the money from your mother is from SS. In the meantime, they most likely will do this. Would suggest mom get her own account ASAP in case they chose to ignore your information about her money being from SS.