I would just dead head them personally.....you should get a 2nd flush of flowers !!!

Poppies such as Papaver orientale well they do die right away, but as they are messy I cut mine right down to the ground after flowering which leaves room for other later flowering plants to fill in the gaps. They will re grow late summer/autumn ready for next year.

I cut my Oriental right back to the ground. If conditions are right they will produce a 2nd flush - not as many as first time round though.

Thank you for your knowledge.