Unplug the sump pump from the electrical outlet.
Cut the bead of caulking placed onto the floor over the joint between the sump pump well lid and the concrete with a utility knife. Remove the bolts from the lid holding it in place using a socket wrench.
Loosen the hose clamp surrounding the check valve with a screwdriver, while holding the valve in place to prevent it from slipping free. The valve will prevent the water held in the exit pipe from spilling out back onto your concrete floor. Pull the pipe extending from the pump free from the bottom of the valve.
Lift the sump pump from the pump well, lid and all, and set out of the way.
Use a wet vac with a hose to remove any remaining water from the base of the pump well. Lower the hose into the hole and turn on the suction, drawing the water from the well.
Clear out the layer of gravel at the base of the well using a spade. Dump the gravel into a wheelbarrow for easy removal from the basement. Remove any water released with the removal of the gravel, using the wet vac.
Take a chisel and place its tip along the outside edge of the pump well. Tap the head of the chisel with the hammer, breaking the bond between the well and the concrete edge. Continue around the edge of the well until you have it completely separated from the concrete.
Grasp the edge of the well liner and pull it from the hole, leaving nothing but the hole in the concrete and the soil beneath.