From Ground: Start with
watering the drooping prickly pear plant which will moisten the soil, making it easier to remove. Gently dig around the plant with a shovel or spade, ensuring you do not cut into the root system. Once you've dug wide and deep enough, start extracting the plant slowly from the ground, preserving as much of the root ball as you can.
From Pot: Water the pot, wait for a few minutes, then place your hand over the top of the plant, fingers splayed around the plant base. Flip the pot upside down and gently pat to ease the plant and its root ball out of the pot. Be extra careful not to damage the roots since drooping prickly pear is delicate during this process.
From Seedling Tray: If the drooping prickly pear is in a seedling tray, wet the soil and carefully slide the seedling out, trying to keep all of its root system intact. Handle the seedling by its leaves and not by its stem.