In what two ways is Romeo the cause of Mercutio's death?

Mercutio was only out and about and likely to encounter Tybalt because he was looking for Romeo. When he meets Tybalt, Tybalt is also looking for Romeo because he is angry and insulted that Romeo attended the Capulet ball. Tybalt intends to challenge Romeo, and as he is known to be an outstanding swordsman, Mercutio has already expressed doubts that Romeo is up to such a challenge.

So, with all the best intentions, Romeo is indirectly responsible for putting Mercutio in Tybalt's path, and although their initial exchange is a duel of words, that quickly escalates into the crossing of swords when Romeo appears and refuses to duel Tybalt. He can't, as he and Tybalt are now kinsmen, but he can't reveal that fact, and this apparent show of cowardice by Romeo infuriates Mercutio.

Mercutio insists of dueling Tybalt. They fight, and Romeo tries to intervene, urging them to stop (the Duke has forbid any more fighting in the streets, and should they be discovered, the Duke would most likely punish even his own kinsman, Mercutio). Romeo manages to get between them and part their swords, but at that moment, Tybalt cheats and stabs Mercutio under Romeo's arm, dealing him a fatal wound.

So, once again, despite his good intentions, Romeo causes Mercutio's death, and this acknowledged by Mercutio when has asks Romeo why he stepped between Tybalt and Mercutio, providing the opening for Tybalt to mortally wound him.

Mercutio blames both Tybalt and Romeo. His curse, "A plague on both your houses!" makes is clear that he held both the Capulets and the Montagues responsible for making "worm's meat" of him.

I would argue, though, that his own mercurial nature (pun intended) played a role in his death. Mercutio was brilliant, witty, and a hothead, and his quick-to-anger nature combined with the heat of a blistering summer day, and triggered by his friend's apparent shame and cowardice, led him to start a fight he couldn't win, whether Tybalt cheated or not.

Mercutio fights Tybalt over Romeo. Tybalt is angry at Romeo for crashing the capulet party. Romeo is trying to appeal to Tybalt but way too hard. His appeals for friendship only make Tybalt more enraged. Mercutio steps in to protect his friend.