"Too deep" can mean too difficult, but it can also refer to something that extends far down into the ground. A mine shaft is a vertical hole, or a horizontal tunnel that gives access to a mine. A mine shaft is often dug deep underground. A mine is an excavation site. The discussion regarding the new mine shaft was "too deep" or "too difficult" for him. The joke is playing on the term "too deep" and its different meanings.
A discussion of digging a new mine shaft was too deep for him .