If vise grip ends up just slipping and stud won't come out, apply heat to the stud, then try again.

Use a blow torch and get as much heat on it as you can. Should come out then.

 

I have never been a fan of using vice grips for getting out a stubborn bolt. You might try a miniature pipe wrench, assuming there is enough to grab on to.

 

Thank you for your help guys ! I was able to take out the broken piece and reinstall perfectly.

Although, you guys must be hercules or something because I could not finger thread in the bolt at all..It took a lot of force.

 

When you broke the stud it was probably due to overtorquing (either now or on some previous instance that stretched and weakened it). So that caused the stud to be wedged into the head tighter than normal. This probably buggered up the threads a little, so new stud was more difficult to put in.