I think mining canals probably wouldn't work - there's too small an area in which to hide them and so they would be found and dealt with very quickly.
Mining the approaches would be a better option, but again, after sufficent time (and resources) were dedicated, they would be cleared.
Such important waterways would not remain blocked by such methods for long. It's in everyones interests, besides those who laid them of course, to clear the way for trade, etc. It could even provoke nations not already in the war (you mined our major trade route!!! BANG!
)