Depends which poppy it is and whether you want to collect seeds from. We leave the seed heads on all our mecanopsis except M. cambrica we dead head this as soon as the flower goes over.

I leave the seed heads on annual poppies as I want more next year. I clear away the dead stems once the seed capsule has opened - and I give it a good shake before popping in the composter.

I hope someone else can advise you if you mean oriental poppies - they just don't like me and flop over and die off before flowering :-(

If you have the papaver oriental poppys then useing some shears cut to the base and it wont be long before new growth is sent up and you may get a second flush of flowers keep well watered once you cut them down, if you want more poppys and they are the annuals then scatter the seed for next year and cut down if you so wish, with meconopsis cambrica they can be very invasive so follow moongrowers advice.