It contains living cells (temporarily), but neither the cells nor the petal fit the definition of an organism: "any complete and entire living thing capable of carrying out all the processes necessary for life."
Technically, the petal as a whole is dead, but the cells within it are more or less still alive for the meantime as they don't die immediately after being plucked. It's like how if you shoot someone in the heart, they're still alive for a moment to a few minutes.
