Try the constrain delay compensation option, and Cubase will disable the most latent plugins in your project. If your project plays fine while in that mode have a look through the mixer insert chans to see which it has disabled.
You may find particular plugins are causing this issue, which may be better routed to group/send to become more efficient channels, or perhaps replacing them for something else which has a lesser effect on performance?
In my experience, It seems that it’s not always just CPU load that can do this, but having plugins with lookaheads and longer processing times can also add stutters - particularly if you’ve got parallel processing occurring. I don’t know what kind of template this is.
I had a whole project fall down because of an EQ plugin which i copied across many channels and had linear phase low cut enabled - made no difference to the sound, but showed up when i applied the constrain mode and lead me to the cause.
Also be careful anything that you apply on the master channel or control room inserts, as it can be a hidden CPU killer.