How to cut OpenBeam/MakerBeam? I'm building a 3D printer and I've been looking around for materials suitable to make the frame.

I have occasional access to a laser cutter which I could use to manufacture a ply box-type (UltiMaker) enclosure, but I like the ease of adjustment provided by the T-slot beam kits.

I don't have any metal-cutting machine tools. Can aluminium beam be cut by hand with a hacksaw to a good degree of accuracy? How does one finish the cut end?
Aluminum of almost every grade is very easy to cut with a hacksaw. I would suggest to mark clearly the cut line and to wrap masking tape at the edge of the cut. Consider to allow for about 2-3 millimeters (1/16") extra material for final finishing. Cut across the line, rotate the part ninety degrees and cut again. Once you have the guide cuts in place, you should be able to manage a square cut by following those guides

You will want to have a clamping mechanism available, such as a vise or workbench type device. 

After the cut is done, use a sharp file to make final adjustments to the length and appearance. Push the file, do not drag it backwards. Push forward, lift away from the work piece as you return, then push again. Pick up a file card, which is a fine metal-tooth brush used to clear the teeth of the file.

It is very easy to remove material with a hand file, perhaps three or four strokes to remove 1/16".

Your accuracy will depend on the measurement of the lines you create and how carefully you file to the edge of those lines.