How quickly does cancer in a mole normally spread?

It depends. There is no easy answer for this. The potential for spread in a melanoma really depends on how deep it is when it is caught and if it is ulcerated (open and bleeding). The deeper it is the more likely it is to have spread. The rate of spread is variable. Predictors of a worse outcome include: male gender, >65 years of age, extremities involvement, lymph node involvement and metastases.
Trick question? I presume you are speaking about melanomas, which often look like a dark mole. Technically, a mole has no cancer, and so won't ever spread. Melanomas come in different varieties. Some grow superficially and don't metastasize quickly, while others may stay small, grow deep, and metastasize widely before the primary cancer is even recognized.