Mitch refers to Morrie as a "religious mutt" because he has created his own religion from a variety of different religious philosophies. The Buddhist philosophy Morrie shares about asking the bird on his shoulder if today is the day he will die serves as a metaphor for his awareness that he may die at any moment. The bird itself is symbolic of Morrie's consciousness that his death is fast approaching, and his readiness to accept it when it does arrive. His lesson, however, pertains more to Mitch than to himself. In telling the parable, he wants Mitch to realize that this bird is on everyone's shoulder at every moment of their lives, despite how young or old they may be. When he tells Mitch that one must know how to die before one can know how to live, he means that one must accept the possibility of one's own death before he can truly appreciate what he has on earth, as the sobering awareness that one day, it will all be out of reach, prompts the urge to appreciate and value what one can have only for a limited period of time, and to use every moment of that time doing something that one will not regret when the bird sings its last note.
When Morrie tells Mitch that he may not be as professionally ambitious as he is if he were aware and accepting of his own death, he is continuing with his idea of time as a precious, irreplaceable gift. What Morrie means by this is not that Mitch should be lazy, but that he should reassess his priorities. He assumes that if Mitch were to truly and completely realize that his will someday die, he would surely rearrange his values system and realize that dedicating his time to love, family, and friends is far more important than spending his life at work, earning money that does not fulfill him. Mitch feels a void in his life which he stuffs with dollar bills, believing that material wealth his what he wants and needs. But Morrie sees through Mitch's superficial desire, and knows that the only salve for Mitch's emotional void is love and friendship.