There is a rumor here at the University of Minnesota that we're called the Gophers because we like to tunnel (and indeed we do, in the winter a student here can get to about half the campus through underground tunnels). Recently, as I was loyally relaying that rumor to a faculty candidate, it was questioned. We immediately looked it up, and found that in fact we are called the Gophers because of a political cartoon that was widely circulated in 1858. This was during a state-wide debate about funding railroads, and in the cartoon the railroad tycoons were depicted as nine gophers with human heads pulling a Gopher Train. Thus we became the Gopher state. Interestingly, the gophers depicted in the cartoon were in fact "striped gophers" or more accurately thirteen-lined ground squirrels.
So tunneling may have had nothing to do with it, but it is kind of a funny coincidence that we are the Gophers, and gophers do like to tunnel.