I use Kynar wire for many projects, which is not easy to strip without damaging the wire itself because it's so thin.
My solution is to lay the tip of the wire on a piece of cardboard, put the tip at the point where I want it stripped, and pull the wire.
This strips the wire perfectly but of course puts plastic on the tip.
This easily cleans off with the damp sponge that comes with just about any soldering station, but if you don't have one, GET one.
Or, get 10 (about $1.29 on ebay - http://www.ebay.ca/itm/Cleaning-Sponge-for-936-12-Solder-Station-5-3-5-0-6-10-pcs-pack-Skin-color-/221407109276?hash=item338ce4609c )
After a number of joints soldered, it's always a good idea to drag the tip across one of these sponges (dampened of course - best to have them in a container about the size of the sponge) and re-tin the tip.
This keeps the tip clean and free of contaminants and allows for easy tinning.
If your tip is too contaminated to be cleaned by the sponge initially, I suggest scraping it with the edge of a piece of cardboard.
Do not wet the cardboard. You basically want to scrape off the contaminants without damaging the plating (most solder tips are copper core with a thin plating of iron or another metal). Dipping the hot tip into solder flux can aid in this cleaning process initially, and will aid in tinning the tip once cleaned.
Alternately, you can simply get another $2 tip for your iron on ebay, and just take better care of it.
If you know you have contaminated the tip with wire insulation, a quick swipe on the damp sponge should instantly remove the contaminants, and your tip will enjoy a long and healthy life.
Always immediately re-tin the tip after wiping on the sponge.
Edited by SuperTech-IT - 9/1/15 at 9:24am