Does the Catholic church allow a previously divorced man to remarry? Suppose a Catholic guy marries a non-Catholic outside the Catholic church, then years later they divorce. Can that Catholic guy get married again to someone else (a Catholic female) in the Catholic church?
Sometimes.

Canon 1059 of the Code of Canon Law states:


  Even if only one party is Catholic, the marriage of Catholics is governed not only by divine law but also by canon law, without prejudice to the competence of civil authority concerning the merely civil effects of the same marriage.


Therefore, the canons concerning marriage in the Catholic Church will be applied to the first marriage.

Now, in this case, the man's marriage will be assumed to be valid in the Catholic Church unless evidence to the contrary is presented:


  Marriage possesses the favor of law; therefore, in a case of doubt, the validity of a marriage must be upheld until the contrary is proven.


(Canon 1060)

And therefore, the second marriage would not be valid:


  A person bound by the bond of a prior marriage, even if it was not consummated, invalidly attempts marriage.


(Canon 1085, section 1)

However, the Catholic man is free to request a judgment for an annulment of the first marriage. Whether or not this would be granted is uncertain, and I can't comment on it in the absence of additional information about the first relationship; it may depend to some extent on the reasons for the civil divorce. If the annulment is granted (i.e. if it is judged that there was no valid Catholic marriage in the first instance) then the marriage to the Catholic woman would be valid; otherwise not.