What role does Mercutio play in Romeo and Juliet's deaths?
Mercutio is the character that sets the fatal sequence in action by baiting Tybalt and drawing his sword. They fight and Mercutio is killed, which leads to Romeo’s killing of Tybalt, which leads to Romeo’s banishment.
Since Romeo is banished, he and Juliet cannot communicate effectively. They fail to carry out their plan properly, which leads Romeo to believe that she is dead when he sees her in the tomb. This leads Romeo to kill himself. This leads Juliet to also kill herself when she wakes up in the tomb and sees Romeo dead beside her.
The whole thing sounds pretty silly in this context. Shakespeare does a much better job of it than I just did. The important thing is that it all makes sense within the play itself, as it is occurring.