It is a good idea to deadhead poppies to keep them blooming and healthy, according to Melissa Lewis for SFGate. Deadheading makes poppies bloom longer and more profusely.
To deadhead a poppy plant, the stem should be pinched under a faded flower between the thumb and forefinger and snapped off. If it cannot be snapped off with fingertips, a sterilized pruner can be used to cut it at this location. This process should be repeated as needed, approximately every three days to keep the poppy from wasting energy making seed instead of feeding flowers. Deadheading should stop if or when seed is needed, typically at the end of the blooming season.