Insulin is chiefly removed by receptor-mediated endocytosis and proteolysis (the receptor organizes a vesicle being pinched off from the cell membrane with the insulin inside, and then the contents of the vesicle can be digested).

Insulin acts by binding to the insulin receptor on the outside of cells, so it isn't otherwise "used up" when it acts. Since a homeostatic signal isn't much good if you can't turn it down/off again, that breakdown mechanism is important.