Whenever a nontoken creature you control dies, put a slime counter on Gutter Grime, then create a green Ooze creature token with "This creature's power and toughness are each equal to the number of slime counters on Gutter Grime."
The power and toughness of the Ooze tokens will constantly update as Gutter Grime accumulates slime counters.
If you control more than one Gutter Grime, each Ooze token remembers which one created it. The power and toughness of that Ooze will be equal to the number of slime counters on that Gutter Grime only.
If Gutter Grime leaves the battlefield, the power and toughness of each Ooze token it created will become 0. Unless another effect is raising its toughness above 0, each of these Ooze tokens will be put into its owner's graveyard the next time state-based actions are checked.