"I will be doing some fancy stitching on TW's "Tea Scene" that requires
some cutting, I would really like to see how you have figured this out
Hopefully, the pattern has lines indicating where you should cut the threads. For the actual cutting, you'll want some small, sharp scissors that will fit easily in the holes of the fabric. I think the scissors that I use are manicure scissors. If there is a lot of cutting, like on the photo below, you will need to take a break because your hands will probably start to ache. Well, at least my hands did. I have fairly large hands and those are such tiny scissors, my hands hurt from holding the scissors rather than the actual cutting.
For a good tutorial on Hardanger, you can go here. There is a great diagram showing where the cutting lines should be.
Here is one of my completed projects that has quite a bit of cutting in it:
This pattern is from the booked Stitched Elegance: Enhanced with Hardanger from Stoney Creek.