Anyone know how to export the groove templates from stylus??

The second method suggested by theRoyal1 is probably the preferred method (by Spectrasonics).
I didn’t suggest that at first for the following reason:
In RMX, Chaos (I know, slightly off-topic) does not export everything as midi to your arranger track in Cubase.
Some of the options require capturing in audio.
I wasn’t sure if the same applied in the Time Designer - hence the quick solution that I suggested.
The way to try out the second option is to ensure that the midi loop you drag to Cubase is what you expect, so:

  1. Pick a loop - nothing to fancy. Drag & drop into Cubase
  2. Now double the speed of it in RMX - drag & drop it again. See the difference in the result.
  3. Go into time designer & select something that makes an obvious change to your chosen loop - drag & drop the midi again into Cubase. Check to see that the result you wanted is in the midi file.

The first method really only shows that there is more than one way to achieve things, but I’d go with theRoyal1 method as the best & easiest option.
Neil