To do an off-shore strike, you need:
1) The capability
2) Politically feasible target
Most of the people who were involved in 9-11 were from Saudi or Egypt? US has the capability to strike against suspects within those two countries, but it's not politically acceptable to hit your own allies. So the US hit Afghan instead because the Taliban was expendable.
The 2008 Mumbai attacks came from terrorists inside Pakistan. Again, India may have the military capability, but it was politically unacceptable to use the military against suspected Lashkar-e-Taiba training camps inside Pakistan. That would risk escalating the incident to a war against two nuclear powers.
If the PRC leadership really wanted to, I'm sure they can send ships somewhere to launch a few land-attack cruise missiles. But there's no politically acceptable targets to hit with the military, nor can you trust some supposed Islamic group abroad claiming responsibility being real -- anyone can create videos and upload them. There are governments, political factions, and even business people who'd benefit from worsened relations between China and Turkey/Algeria/etc.
If Beijing primary concern is Xinjing breaking away, then the simple solution would be to send sufficient immigrants to the region and take away that possibility. Compared to other past Imperial powers, China is one of very few that was able to come out of 19th-20th century with the majority of its territory intact. The PRC is the 3rd or 4th largest country in the world today and there's still much territory that is under-developed. Rather than looking across the sea, perhaps the government should invest more effort in the "Go West" program to settle the 60% under-populated regions of China.
Bumping people off is a short-term fix, vs. settling Xinjing with people is the long-term solution. Rather than sending migrants into existing cities and clashing with long-time Uighur residents, maybe planning and creating brand new cities dotted across Xinjing would be better? As a LAST resort, allocate a Singapore-sized piece of territory and send all the Uighur nationalists there -- you can have your own territory but you must stay on your side and we'll stay on our side. You cross the line to cause trouble, we shoot you.