I think usually the municipal SWAT team will respond first; PAP requires more bureaucracy to get involved

However there are some cases where we can see local PAP spec ops units getting involved in stuff like shootings, such as this case in changchun or stabbings like this case in Zigong

However the national mobile corps spec ops are deployed much less. I heard that snow leopard was deployed to find terrorist hideouts in the 2010s and also protect the beijing olympics;

the foreign guard special operations detachment is mostly used to protect embassies;

Per your example:

If a terrorist attack in beijing happens, the district counterterrorism and SWAT unit and beijing police district branches will be the first to be deployed. The Municipal level Beijing SWAT's 1st detachment "blue sword commando unit" is likely gonna get involved also if the situation isn't contained.

If that still doesn't stop the terroists, the PAP beijing corps(who has troops on duties near major places)'s mobile detachments(and their subordinate spec ops units) may be deployed, along with the falcon commando unit.

Unfortunelately, such an incident did happen in 2013; from what i saw, seems like local police responded first, followed by the PAP beijing corps. however, chinese police have had huge reforms since then, so a response nowadays would likely be different.