“Tempt not a desperate man”

Romeo believes Juliet is dead and is standing by her grave when Paris comes across him, accusing him of her death and challenging him. He's despondent, despairing, and enraged. He's come to view Juliet's body and commit suicide so that he can be with her in death.

Paris attempts to "apprehend" Romeo, who has been exiled from Verona for assassinating Paris. Paris informs Romeo that he "must die," and Romeo replies, "I must truly," meaning that he intends to die tonight in some way. He then warns Paris not to "tempt not a desperate man" implying that he should not tempt him to fight since a desperate man is a deadly opponent.

The fact that Romeo no longer wants to live proves that he is "desperate." Juliet was "the sun" in his life, as he explains early in the play. There is no longer any warmth or light in the world without her. As a result, he believes he has no purpose to live. He wants to die, but he also wants to see Juliet one more time. He assassinates Paris for this reason. After hugging Juliet's body, he consumes poison and surrenders his life to the "dashing rocks" of death.

Romeo - Act 50, Scene 3.