It isn’t a ligament. It is a muscle.
It is a lateral rotator of the upper arm and as such it swivels the head of the humerus in the socket away from the body as one of its major actions. (A medial rotator would rotate it towards the body).
There are lots of exercises i can give to rehab it, but you need to stretch it in a controlled manner too, exercise light and controlled depending on the severity of the injury (not too severe if you are deadlifting and exercising as normal IMO) and you would benefit massively from some deep tissue manipulation, frictions, stripping (no), whatever - again depending on the grade of the injury and your recovery.
If it is totally severed, there should be a bunching up of the muscle just above the shoulder blade, or below the upper trap. I doubt it is… but seeing as someone suggested surgery and you are not too hot on basic physiology it is possible i guess.
Lie on your healthy side. keep your injured arm pressed against your side and thigh. Slowly lift the arm so it is perpendicular to the body.
If you can’t get it off the thigh then it is torn off the bone.
Then stand up straight, with your arms out to the side. Position your hands as though you are holding two cans of soda open and out to the side. Then pour the soda out by tipping your hands forward, then keeping the same position of the arms and body, tip your hands to the rear - as though pouring the soda out of the can backwards.
If your supraspinatus is injured it will hurt mostly as you tilt the hands to the rear. It would have also hurt as you lifted your arms up too!
Rehab is a bit more than just avoiding the lifts that work that muscle, which is why i recommend going to a professional. Do you pull your own teeth? Then why try to rehab yourself when you don’t know what you are doing?
I stand by my first advice that i gave last time. Go to see an injury specialist.