Without more context I will be guessing a little here. But I will try. I'm gonna just put mine off to the side. I am simply going to put mine off to the side. gonna = going to (construction to show the future tense) "put mine off to the side" could have different meanings, depending on the context. "To put something off" can mean to leave it until later. However, the addition of "to the side" at the end maybe implies a more literal meaning of physically moving something out of the way.

Just ignore my stuff and focus on something or someone else more important ?