Pests may hide in mandevilla foliage, but you don't want to bring these indoors. Spraying the plant down with a sharp spray of water, paying special attention to the underside of the leaves where pests tend to feed, rinses them off the plant. Remove any dead or damaged foliage before you dig, and pot the mandevilla so you are only transplanting the healthy plant.
Keeping as much of the root system as possible improves the chances for plant survival. Dig around the perimeter of the root ball, beginning 10 inches away from the base of the stem. Dig down 10 to 12 inches, or until you are beneath the root ball, then lever it out of the garden bed. If you must grasp the mandevilla to lift it, hold the main stem just above the root ball. Don't try to pull it up; instead, use the spade to lift the root ball out of the ground.
The size of the pot depends on the size of the mandevilla, but most thrive in 1- to 3-gallon pots. Select pots three inches larger in diameter than the rootball. The pot must have bottom holes to provide water drainage so the soil doesn't become soggy. If necessary, trim off up to a third of the outer roots and cut back the entire plant by up to a third its height to help it adjust to the root loss. Pot mandevillas in a well-drained, standard potting soil, setting them at the same depth they grew in the ground and with the top of the root ball two inches beneath the pot rim. Add a stake or small container trellis to the pot to support the mandevilla, or plant it in a hanging pot so the vines trail over the sides.
If you pot mandevilla to overwinter it indoors, set it in the sunniest location available and maintain a temperature above 60 F. Water the soil when the top inch feels dry, and empty the water that drains from the bottom of the pot into the drip tray following each irrigation. Outdoors, potted mandevillas may require daily watering if the top inch of soil dries quickly. Trim the top of the plant as needed to keep it a manageable size for the pot and trellis. Remove dead stems or leaves as necessary.