What is the effect of the line "Boy, this shall not excuse the injuries that thou hast done me"?

This comment is Tybalt's response to Romeo's cryptic explanation, in act 3, scene 1, of why he will not engage in a fight with Tybalt. In order to fully appreciate its effect, we need to look at the language used before this line. Note that Mercutio uses formal, polite pronouns when he speaks to Tybalt: "your livery," "your worship." In the language of Shakespeare, this differentiation between "you" and "thee" is often very important. The use of "thee" can indicate either familiarity and fondness or, in other contexts, contempt. Mercutio is not a friend of Tybalt's, so he uses the formal "you" pronoun in recognition of Tybalt's social status and their lack of intimacy. When Romeo addresses Tybalt—"the reason that I have to love thee"—he seems to be using the informal pronoun as a means of currying intimacy between the two, hinting at the unspoken tie which now binds them. Romeo is attempting to calm troubled waters, bidding Tybalt "farewell" and refusing to engage with him in a fight. However, this is not at all how Tybalt hears what Romeo is saying.
On the contrary, the sharp, rebuking tone of his response—"Boy, this shall not excuse the injuries / That thou hast done me"—suggests that he is cutting Romeo down to size. In response to Romeo's intimate pronoun, he calls him "boy" to underline his feeling that Romeo is being presumptuous in addressing him in this fashion, the suggestion being that Romeo is younger than Tybalt. Tybalt's own use of the "thou" pronoun, in connection with this "boy," carries contemptuous overtones. Rather than calming Tybalt's ire with his gentle parry that "villain am I none," Romeo has only provoked Tybalt further, with Tybalt insisting, "therefore turn and draw."