Can I be admitted into a grad school program at a different university if I quit my current program?
With poor grades, it will be very difficult to get accepted at another program unless they are in in different fields (i.e., you could argue that during the course of the MS in psych, that you discovered that you have no talent for psych and that you want to go into a PhD for architecture or astrophysics). But that isn't the case for you.

However, you should know that you do not have to withdraw from your MS in order to apply to PhD programs. You can stay in your MS and apply to PhDs. You should note this in your application and state your intention to withdraw from the MS if you get into the PhD.

It will help your application TREMENDOUSLY if you can get a faculty member at your current institution to speak to why your performance was poor but that you have a latent talent that isn't reflected in your grades.

I should note that the likelihood that PhD programs will accept you given the poor grades will be pretty slight so I would not get your hopes up too much (or spend too much time and money applying to other programs).

Most "transfer" type students that we accept at the PhD level tend to want to transfer because of: 1) their original program is dissolving; 2) their adviser has left (either physically or mentally); 3) other issues about the original program that was not apparent when they applied.