Are you supposed to cut off the solder wick before or after you use it?

The temptation is to desolder an area and keep moving up the spool of braid. However, it’s best to work towards the end of the braid to isolate the heat. Once the desoldering braid is brought up to soldering temperature, the flux has been fully activated, so that part will not draw more solder. A long strand of used braid only acts as a heat sink, slowing down your process.