Can I invite my mother from Mexico to visit me in the USA even if I am illegal in the USA?

No.

There is really no such thing is inviting. She can apply for a visitor's visa and if she qualifies and is granted one, then she can come into the US for a brief visit.

Your mother can apply for a visitor visa, but it is not likely to be granted if she has children in the US that do not have lawful status.

In some countries such invitations have a legal effect, but this is not really the case with the U.S. Inviting someone to visit the U.S. can only entail writing a letter addressed to the consulate and submitting Form I-134 and providing evidence of income and/or assets. The consulate officers typically give little to no weight to such "invitations". Your mother can apply on her own. It doesn't help that her that her son is here without status, and I don't think there's anything you can do to increase her chances of obtaining a visitor's visa.