I´m a industrial design student currently trying to make a box cutter, it´s a rather simple one, but for some reason the fillet doesn´t seem to work.
I´ve tried "Composite curves", I´ve tried changing the radius of the curves, and still nothing. In the middle part of the box cutter it worked just fine, but I can´t find out why it doesn´t here.

Try unchecking “tangent” and then select one edge at a time, or try using the face option or conoc option. If that doesn’t work then you may have to try variable or reducing the radius.
hope this helps.
If it didn't work, just make a swept-cut along the edge of your model, where the profile will look like this:

It may be impossible to say for sure without looking at the model, but I'd place my money on one or more tiny segments near the selected edge.
Try picking the flat model face which has the blade passing through it. Doing so will affect all of the edges (assuming there are some tiny, invisible ones there).
Also try changing the radius value to a smaller number (1mm) and seeing if it starts to work. a 21mm fillet on the front of a handheld tool seems very large.
As stated above, try a small radius and then work up in size until it fails. Is the protruding blade a separate feature? or is it all one solid. If it is all one solid, the radius maybe struggling to blend into the square edges of the blade. Try blending the handle, then add the blade last.
What do you mean by "surface in the fillet"?
Check out some of the techniques shown here:
http://dimontegroup.com/solidworks-world-2014-will-blend/
There may be some newer presentations as well, but this one came up first.
The basic idea is trimming away the sharp edge, they manually building the fillet with surface tools before knitting everything back into a solid.
Amazing techniques.
Thanks for sharing.
Filleting = Rounding-off edges
Non-filleted pole (left) and a filleted pole (right):
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Split the part in half (best to use cut with surface and select the center plane as surface)
apply the fillet
mirror the bodies
Filet is rounding edges, faces, etc.