That'll work fine on copper or brass. On steel (which, I think, is what most hypodermic tubing is made of), knife blade will have trouble; if it does eventually cut the tubing, the blade will probably be rendered uselessly dull in the process.
I know of two other ways to tackle the problem. If the tubing isn't too fine, you can shove a piece of appropriate-size piano wire through it. Then cut the tubing, and the wire inside, with a good, heavy pair of wire-cutting pliers. The pliers are highly unlikely to crush the wire; it should slide out of the cut tubing.
If the tubing's too fine to push the wire through, try an abrasive disk in a fairly-fast-turning rotary tool. That should give you a nice, clean cut.
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