When I smoked cigars on a regular basis, I chewed them as much as I smoked them. I'd smoke one halfway down, let it go out, and chew on it for an hour or so before finishing it. At least that's how I did it at work. I had a cigar, lit or unlit, in my mouth most of the day. So, it was a no brainer to use my teeth, generally taking a while to gnaw it off just right while going about my business.
After work at home, it was usually a better cigar or a pipe.