Death Penalty (DP) is based on your highest level, up to around 460,000 for a character with a skill level of 250. DP stacks up to 10 deaths.
You remove DP by performing actions, removing DP at a rate of (skill used level / 10) * xp gained. The highest skill does not necessarily remove DP faster - the one that gives you the most XP does.
DP slowly wears off with time (although very slowly) and it's possible to buy special gifts (pacts) from Ma-Duk or Jena at altars to speed up the process. These are useful to buy if you are logging out and still have lots of DP yet to recover.