Yes, Minesweepers would be included in the game. Ever since the advent of mines there have been military units dedicated to the creation and elimination of minefields. An Engineer unit could constitute the land requirement, as well as take on multiple other tasks such as construct firebases/fortifications that add a small bonus to defense and can be built relatively quickly and inside enemy territory; and convert roads to be usable by friendly units in hostile terrain. That's always been a pet peeve of mine, why wouldn't my units be able to use enemy roads? Ofcourse I realize that it is a required mechanic for a game such as civ, however there comes a point where that mechanic needs to be modified. An engineer unit could 'work' an enemy road and allow movement on it, in the same timespan (or slightly longer) that a worker can build a normal road.
If no engineers are available, an artillery barrage could degrade the minefield much like city defenses. This works in the real world.
A sea variant would include a surface mine laying ship, which in modern ages can be outfitted with cruise missiles to give it some defensive firepower (simply a thought). Submarines could even fill the role as they have in the real world. Perhaps you could simply build a mine package and load it onto a Destroyer or Sub. A special promotion could be available for Destroyers which would allow you to specialize a few in the removal and deployment of minefields, and thus there would be no need for a new sea unit. Also a bombardment from naval units could degrade the oceanic minefield much as it would on land.
Lastly air deployed mines are also an option, as both sea and land fields have been created in this manner.
The key would be to make every unit NOT able to clear a minefield, for obvious reasons. The reality is that mines are cheap, easy to use and quickly deployed. They also require expensive countermeasures in the forms of specialized units (or a massive concentration of firepower) which is exactly what makes them so effective. They are on par with the creation of artillery, the rifle and the advent of combined arms warfare in the influence they have had on human conflict. To have them not represented in Civilization is unacceptable.