They certainly can. A recent study evaluated the results of this procedure ("partial meniscectomy") in 91 patients with an average age of 74. More than two-thirds of the patients had less pain after the procedure. Roughly four years later, these patients hadn't had more surgery. They said they were satisfied with their results and would choose the procedure again.
Of course, these results aren't as good as those commonly seen in younger patients. In general, researchers think that patients over 70 should proceed with caution when it comes to knee surgery. This is especially true for patients who have more knee arthritis or cartilage damage.