Is there any way to reduce the duration of Grievous Wounds?
No, there is no way to remove or reduce the duration of Grievous Wounds in the current patch.
In previous patches, you could buy Quicksilver Sash. It's active effect removed all debuffs from your character, including GW. However, it now only removes CC (crowd control), or movement-impairing effects.
Also in previous patches, Soraka's ultimate, Wish, would remove GW before applying its healing effect. That was also removed, however.
Tenacity only affects some CC effects, and GW does not count as CC, so that does not reduce the duration either.