What do you call the exploitation of ambiguous statements to form a logical argument?

Solution 1:

From Internet Encyclopedia of Phylosophy

Faulty Generalization

A fallacy produced by some error in the process of generalizing. See Hasty Generalization or Unrepresentative Generalization for examples.

Solution 2:

First of all, the two conclusions that you draw do not come from

Men commit more crimes than women

but from

Every man commits more crimes than any woman.

Without qualifiers (all, some, none) the proposition can mean that men on average commit more crimes than women.

Secondly, regardless of what is actually the initial phrase, to talk about fallacies you should have some reasoning which you do not present, you only present a simple proposition.

EDIT (after question clarified)

In rhetorics the vice of ambiguity is called simply that - ambiguity (related terms: amphibologia and also ambigua).

In logic the incomplete comparison might be the correct term.

Once you have established a logical fallacy in the premise that should (normally) be enough to classify the conclusion as faulty, too.