I have a 5.0 F-150 with broken rear leaf spring mounts and I am wondering if those could be causing an issue with my transmission. Currently having a vibrantion on deceleration.

 

Could be. It depends how bad the broken part is and where the vibration is coming from.

Slowing down may be causing the rear axle to angle slightly because of the drag braking/slowing cause with the ground. This would make the rear end out of alignment and vibrate.

It would be best for fix the broken mount to see if it goes away and for safety sake.