This pro life tip brought to you by The Irritation of Removing Uncomfortable Tags.
Use a seamripper to remove the stitches that attach a tag and the garment itself. See attached picture for a demonstration of this. Seamrippers are cheap (~1 USD is typical) and available at any store with even a token sewing section, such as walmart or target, and some grocery stores as well. Using a seamripper lets you remove the tag entirely, while cutting the tag off usually leaves behind a sliver of the tag fabric that can be uncomfortable.
Probably far quicker and less likely do damage something else. Seamrippers work by having a small blade in the middle of the U-shape. And due to the pointy bit at the bottom, you might be able to more easily scoop up the thread if it’s tighter