Shulchan Aruch (O.H. 551: 2) prohibits to plant a "netia shel simcha" (planting done for aesthetic or joyous purposes). However, Mishna Berura (ibid. 13) permits the necessary maintenance of what is already there, to avoid any losses.
It is therefore permitted to do basic garden upkeep, to cut the grass, weed and water the lawn/flowers, since these activities are only upkeep.
Rabbi A. Bartfeld as advised by Horav Shlomo Miller Shlit”a