Using a sewing thread, tack around the area from which you want to remove threads.
In the middle of the area, pick up just one thread of the fabric using a tapestry needle. Slide the scissors under the same thread next to the needle, and snip the thread.
Thread the needle with the first unpicked thread and weave it back into the fabric.
When you finish weaving all the unpicked thread into the fabric, you can start trimming away the excess thread.