Romeo fears that the evil outcomes or "black fate" of the violence of Mercutio's death lies in the future. The woe or misfortune and grief will not end today with Mercutio's death, but will have repercussions in the future. This foreshadows the tragedies that unfold within the play. Romeo is saying this is just the beginning.
In Romeo and Juliet the Capulets (Juliet's family) and the Montagues (Romeo's family) hate each other so much that it seems there can be no compromise. Romeo and Juliet have decided that their love can reach well beyond the feud and have secretly married. Therefore, Romeo knows that he cannot accept Tybalt's challenge as Tybalt is Juliet's cousin and so he tries to tell Tybalt in Act III, scene i that he loves him "better than thou canst devise" (67) because now they are related but Romeo cannot share this information freely.
Mercutio thinks that Romeo's actions are "dishonorable" (71) because he does not know that Romeo has married Juliet and Mercutio dies at Tybalt's hand as he accepts what should have been Romeo's fight. Significantly, Mercutio curses "both your houses" (89). Romeo cannot believe what has happened and blames this terrible event on his love for Juliet which he claims has made him "effeminate" (111) and he knows what he has to do.
When Romeo says in lines in lines 116 to 117, "This day's black fate on more days doth depend; this but begins the woe others must end" he suggests that he is not in control of his own fate and he recognizes that there can be no acceptable outcome. His words foreshadow what will follow. Even though Romeo tried to avoid fighting with Tybalt, he is now suggesting that fate will ultimately control the day's events and everything that ensues. He feels powerless and says that Mercutio's death has effectively sparked even more distress but others will have to resolve the matter. His fighting with Tybalt will only start something else. Whenever one issue is settled, it starts another.