Mucus with diarrhea may be also in diverticulitis (infection of diverticula, which are most often in the descending colon, so on the left side of abdomen), intestinal worms, inflammation (Crohn's disease or ulcerative colitis).
If that green color was from bile, you'd probably feel some anal burning during bm.
You shoul have a stool test for parasites (giardia) and stool culture, including the test for Clostridium difficile.