Getting gum off a sweater sounds tricky, but there are some simple methods to fixing this sticky situation. There are several recommendations for removing gum, but the easiest and most effective way is to freeze the gum before pretreating the sweater and washing.
Lay out the sweater on a table or in a sink, with the gum stain facing upward. Take a few ice cubes and place them over the gum. Place a plastic sandwich baggie over the ice as a barrier and set a heavy book on top to press the ice downward. Wait 20 minutes.
Remove the book, plastic sandwich baggie and ice. Make sure the gum is completely frozen. Use a pair of tweezers to gently pick off the hardened gum, using a steak knife to cut any fibers from the sweater that are being pulled excessively.
Rub some enzyme laundry pretreatment over the gum spot, using the sweater itself to rub in the pre-treatment in. Wash and dry as usual.