Leak in wall behind sink

I discovered a leak in the wall behind my sink. The tee connection to the vent pipe is broken. Will cutting out the tee and replacing it with a new one be sufficient? Is there anything else I need to be concerned with before I cut it out?

The condition of the rest of the pipe would be my only concern.

The horizontal pipe comes through a 2x4 jsut 6 inches from the connection. There is no give at all. Should I cut a little around the pipe to give it a little wiggle room? I wonder if it the lack of give contributed to the break.