Romeo says to Paris, "Good gentle youth, tempt not a desperate man." How does he feel about himself at this point in the play?
At this point in the play, Romeo believes that Juliet is dead. He is desperate, hopeless, and angry. He has come to the Capulet tomb to see Juliet's body and to commit suicide so that he can be with her in death.
Paris tries to "apprehend" Romeo, who has of course been banished from Verona for killing Paris. Paris tells Romeo that he "must die," and Romeo responds, "I must indeed," implying that he means to die this night, one way or another. He then tells Paris to "tempt not a desperate man," meaning that Paris should not tempt him to fight, because a desperate man makes for an extremely dangerous opponent.
The fact that Romeo no longer wants to live confirms that he is indeed "desperate." Juliet was, as he says earlier in the play, "the sun" in his life. Without her, there is no warmth left in the world, and no light. He therefore feels as if he has no more reason to live. He is desperate to die, but he is also desperate to see Juliet one final time. For this latter reason, he kills Paris. He then drinks a poison after embracing Juliet's body and commits his life to the "dashing rocks" of death.
Throughout this whole scene, of course, the audience is aware that Juliet is not dead at all. This dramatic irony makes Romeo's desperation more pitiable, and it is all the more tragic because it is predicated on a false belief.
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