Rear rockshox thru axle. How to remove it if skewer got broken off?
Assuming your axle looked a little like this before the break. 



Purchase a new 12mm thru axle of appropriate width for your bike. It is nothing to do with RockShox on the rear axle. Check your bikes spec on the internet or original supplied manuals. 

Unscrew the handle from the new axle and use that to undo the splined axle from the original. Once you have done that replace the handle on the new axle and install on the bike. 

A couple of issues. 


The splines on the original axle might not be the same as the new one unless you get exactly the same brand. If you have access to a LBS this might be the time to use one instead of internet mail order. 
Rear axles are sometimes fairly tightly screwed in. Ensure you are careful to not injure yourself or ruin the spline by skidding off the unsecured handle when removing it. Wrap the handle in a rag and apply pressure along the axis of the axle with your palm. Maybe lie the bike flat to do this task. A soft mallet may come in handy to break the initial friction as well.