It has acceleration while it's in your hand and you're in the process of flinging it, but we don't know how much.
It has acceleration ... pretty big ... during the short time between hitting the first blade of grass and coming to rest in the dirt, at the end of its trip.
From the time it leaves your hand until it hits the grass on the way down, its has the same constant, continuous acceleration ... 9.8 m/s^2 downward, the acceleration of gravity.
The greatest acceleration is probably at the end of the trip, after it hits the grass, and its speed drops to zero in a tiny fraction of a second.
