No problem. Once you actually have it set up correctly you will need to hit the delete button to move the message to your locally set up trash on os x mail, and then delete it a second time from the os x trash to actually get rid of the message...and do not quit os x mail immediately because it takes a few seconds to have os x mail communicate with gmail to actually delete the message from gmail's servers.
Like I said, convoluted.
Why have apple and google made it so difficult to actually delete the mail one wants to get rid of?...Good question, huh?