The Earth is also a pretty good object for sending signals back to the radar. If you point the radar at the ground, you'll get a strong signal. So naturally most people don't point the radar at the ground. But that doesn't solve the ground clutter problem, because if you point the radar low to the ground, part of the beam will intersect the ground and produce a return signal. On the other hand, if you point the radar well above the ground, you miss seeing all of the precipitation near the horizon at larger distances from the radar.
The National Weather Service radars take advantage of a useful fact: the ground doesn't move. Thus, the ground clutter falls into a known pattern which repeats itself. Also, the Doppler velocity of the ground clutter is zero. The radar processors use this information to detect and identify ground clutter and remove it from the display. These techniques are not perfect, though, so you should be alert for radar echo patterns which don't move.