Would be nice to know the type to be sure but in virtually all cases, yes. Perhaps wear gloves when doing it as the milky sap produced when cut can be caustic and if it gets in your eye, very painful.

If the old blooms are dead , cut them off at the base, but be careful as 'FRACTAL' says. Presume you mean 'Euphorbia'?

'Euphoria' is a state of mind.