Cutting stock recursion
void function

The bibesCutter itself doesn't care how many bibes have been claimed already. It only calculates how many are needed for the remaining requests. Therefore I'd recommend to change its signature to

int bibesCutter(Vector&lt;int&gt; &amp; requests, int stockLength, int &amp; rest)

Recursion

The first recursive call to bibesCutter always falls into a base case (tmp has exactly 1 element). I suppose it is much cleaner to deal with it inline. At least you'd spare creating and destroying a vector.

Once this is done' you'd notice that a code becomes tail recursive, so the recursion could be eliminated at all.
Correctness

It would be nice to prove that the algorithm yields the optimal solution. The request to fulfill with the remaining piece of pipe (toCheck) is selected pretty much at random. That, along with the above observation on recursion elimination, is a red flag.
Misc

tmp and toCheck are not best identifiers.

stoclLen is a very funny typo.