Question

Why does Romeo blame himself for Mercutio's death?

Answer 1

When Romeo and Mercutio are faced with Tybalt, Romeo decides not to fight him because he is Juliet's relative. He does not want to cause more problems between the families, nor any grief to Juliet. However, this means that Mercutio has to defend Romeo, and he ends up being killed by Tybalt. Romeo, therefore, feels very guilty because he placed his love for Juliet before loyalty to his friend.

Answer 2

Tybalt is angry at Romeo. Tybalt wants to fight Romeo. This happened right after Romeo and Juliet got married so remembering that Tybalt is Juliet's cousin, Romeo decides not to fight. Tybalt provokes Mercutio and the two fight. Mercutio looses and Romeo is crushed. If Romeo had told Mercutio what was going on, Mercutio would not be dead and neither would Tybalt. That is why Romeo blames himself for Mercutio's death.  Romeo chases Tybalt and kill him. Romeo is then not executed, but banished. 
I hope this helps. It has been a while since I read the story. :)