It says here that
One is not allowed to use a comb on Shabbos to comb his hair because one will ultimately pull out hair while combing. This is forbidden even if one will only run through the hair lightly with the comb.
EDIT: R' Sholom Yehuda Gross says (in Ch.1 P.1):
The overwhelming majority forbid all methods of removing the beard, including the use of sissors (which is sometimes misconceived as being permissible).
(Ch 1. P.3)
Many poskim [quotes Tosfos, Beis Hillel, Maharsham, Darkei Tshuva) forbid the removal of the beard even by means of a depilatory powder (chemicals applied to the skin to remove the hairs) since this is also viewed as a transgression of the Biblical prohibition against removal of the beard.
Yet, he writes that one is allowed to comb his beard on a weekday.
Why does he allow it? If anything, on Shabbos there should be a bigger Hetter to comb, as one needs a Meleches Machsheves to be considered Mechalel Shabbos. Yet, it is considered to be a psik reisha that one will pull out hairs. If so, why is one allowed to comb his beard during the week?
EDIT This question is only true according to those who say that removing hairs from his beard in any way violates a prohibition.