Outside of QuakeEdge and X-scissor, Excadrills movepool is pretty barren so anything that resists those 3 core moves(or even just QuakeEdge) can take on Excadrill. Heatran with the Air balloon makes an excellent lure for Excadrill. All it has is feeble Rock Slide to cause damage. It gives Heatran a free turn to setup or Fire Blast away.
Changing the weather is another good way to stop Excadrill. Politoed is probably the best way to get rid of Sandstorm thanks to it's Rain-boosted Surfs. However it can only switch-in safely if the Excadrill is using Swords dance or Rapid Spin. Unless it invests heavily in Defence it just doesn't have enough bulk to take boosted EQ. The weather changes no matter what though, making it a lot easier to take down. Ninetales and Abomasnow can do it too but not as good as the Toad.
Like many sweepers, 'Drill does not like paralysis or Burn. Serperior with Glare, Rotom-A, Dusclops, you should know these guys by now.