Poppy flowers consist of over 200 different species, divided into both annuals and perennials. The perennial varieties can quickly spread and crowd out other desirable plants. If you are trying to get rid of a perennial poppy species, you must kill the underground root system as well as the above-ground portion of the plant. Killing the poppy flower roots requires a combination of mechanical removal and smothering the root portions.
Put on garden gloves and pull up as many of the poppy plants as possible, placing them into a trash bag for disposal. Although this does not kill the root system, it prevents any seeds in them from dispersing and growing more flowers.
Rake off any mulch in the area. Push it over to the side of the planting site.
Set a garden tiller blade to at least 6 inches deep and place it at the edge of the planting site. Start the tiller and push it over the entire area to chop up any poppy roots that are in the soil.
Spread newspaper over the entire planting site overlapping each section so that no soil is visible. Dampen the paper with a garden hose and alternate the process of laying paper and wetting it until you have 15 layers installed. The newspaper smothers any poppy roots that attempt to grow back.
Rake the mulch back over the area using a rake. If there was no mulch originally, purchase some and distribute it evenly over the area to disguise the newspaper.
If you have other desirable plants nearby and cannot till the area, you must dig up each individual poppy root using a shovel or a hand spade.