I want to build a cyclocross-type bike for bike path type riding. I have a road frame and mtb fork for 26" wheel. Can I use these together, with flat bar/front cantilever brake&26inch wheel, rear no brake and 700c rear wheel, like an old style time trial bike? The frame already had slow handling, so I'm not worried about slow handling.

If both the frame and fork are the same size headset diameter then there is absolutely no reason why they wont work.

I'm going to assume this is a suspension fork. You may not have clearance between the top of the fork and the down tube but this wont matter unless you are doing bar spins.

If it is a rigid fork you may be able to get a 700cc wheel and tire to fit.

this is a rigid fork.

Go for it, what is the worst that can happen? The bike might steer a little slow but that is all i can think of.

Oh and it might dictate what kind of brakes you can use.