Gutter Grime has an ability that triggers whenever a nontoken creature you control dies. When this triggered ability resolves, you put a slime counter on Gutter Grime and a token creature into play that has power and toughness determined by the number of slime counters on the Gutter Grime. This power and toughness is continually calculated, as the token creatures are given an ability that constantly checks the number of slime counters on Gutter Grime.

Because the token creatures created by this ability ‘look’ at the Gutter Grime to determine some characteristics, if the Gutter Grime leaves the battlefield, there is nothing there to tell you the power and toughness of these creatures. This means that these token creatures will have a power and toughness of 0/0 and they will end up going to the graveyard.

Keep in mind that each individual Gutter Grime applies to the token creatures that it creates. If you control two Gutter Grimes and one is destroyed, only those token creatures that were put into play via its ability will end up going to the graveyard.