Cull (v.)
reduce the population of (a wild animal) by selective slaughter.
On Merriam Webster, meaning ‘to reduce or control the size of (something, such as a herd) by removal (as by hunting) of especially weaker animals’ “the tool, Wind Sand and Stars“, by Antoine de Saint-Exupery.
“…gentler than the culling of a flower…”
culling sounds a bit similar to killing, which this words definition closely resembles , so the sentence means Killing a flower or a bunch of flowers.