Prepare the target location for the blue agave before attempting to dig it. Choose a well-draining site or prepare a large pot with a 1:5 mix of organic and inorganic matter, such as sand. Wait to dig the agave until the fall if at all possible.
Mark a circle at least 6 inches away from the outer edge of the agave. Dig straight down with a sharp shovel around the circle, being careful to completely sever any roots that are outside of this zone. Dig any pups that may have developed on rhizomes outside the circle and transplant or discard them.
Prune any damaged or diseased roots before transplanting the blue agave to its new location. Plant the agave so the crown is even with the soil level. Resist the urge to water a fall-transplanted agave, but water spring-transplanted agaves every four days for the first month after transplant. Shade and gradually harden off spring-planted agaves.