Operation Phoenix is one of Rick's many crazy experiments.
This experiment began at some point before Big Trouble in Little Sanchez. While testing it, Rick transferred his mind into a clone named Tiny Rick to hunt a vampire at his grandchildren's school. Unfortunately the side effect of the younger clone is that its brain starts to override the original Rick's personality. At the end of Big Trouble in Little Sanchez, Rick (completely naked and fresh out of the preservation chamber) presses a button, taking Morty and Summer down into his underground dungeon (also seen in Auto Erotic Assimilation) which is revealed to hold several chambers containing Ricks in varying stages of development. Rick proceeds to viciously butcher his many clones with an axe to his heart's content, stating the experiment was a failure.
In Edge of Tomorty: Rick Die Rickpeat, the purpose of Operation Phoenix was revealed. When Rick dies in any dimension, his mind is automatically uploaded into a clone body. Rick had replaced this protocol by having Morty put a tissue sample from his corpse into a cloning machine. He did not know that he would be revived by Operation Phoenix in other dimensions whose alternate Ricks had proceeded on with the experiment. Every time Rick died in this episode, his backup was rerouted into a different dimension's clone vat. Unlike in Big Trouble in Little Sanchez, Rick's personality stayed the same, either because the alternate Ricks had solved this problem or because Rick did not spend a long enough time in one body for it to happen. The episode does not show whether Operation Phoenix can successfully revive any other Ricks, even its own creators like Fascist Rick.