In Act III Scene III, Antonio pleads for mercy, but Shylock is deaf to his pleas. He declares that he will have his due from the bankrupt Antonio, no matter what Antonio says.
Shylock claims that the duke will grant him justice, and since Antonio has called him a dog before he has had reason to, Shylock advises him to be careful about his fangs. This just means that Shylock wants to exact retribution against Antonio for previous insults: if he is going to be known as a dog, he will definitely make his fangs felt.
I’ll have my bond. Speak not against my bond.
I have sworn an oath that I will have my bond.
Thou calledst me dog before thou hadst a cause.
But since I am a dog, beware my fangs.
The duke shall grant me justice.
In Act 1, Scene III, Bassanio wants to borrow three thousand ducats from Shylock. He promises Shylock that Antonio will guarantee the loan. However, Shylock hates Antonio because Antonio is a Christian who lends out money without charging interest. In Shylock's mind, this sort of practice cuts into his profits as a moneylender. Antonio, for his part, states that he is not in the habit of borrowing or lending, but that he will break with precedence to furnish the needs of a friend.
However, before consenting to lend the three thousand ducats to Bassanio, Shylock toys with the men. He sneers that the people who used to spit on his 'Jewish gaberdine' and call him a 'misbeliever' and a 'cutthroat dog' now want to borrow money from him. He wonders if a 'cur can lend three thousand ducats' and demands to know why he should lend money to those who are fond of calling him a 'dog.' Antonio responds that he will likely call Shylock the same thing again and tells Shylock to lend Bassanio the money as an enemy, not a friend. This way, if Antonio fails to come up with the money, it would be easier for Shylock to collect his due, implying that he would not need to trouble his conscience with any guilt on his part.
Shylock then jovially says that he is willing to lend Bassanio the money at zero interest; the only catch is that Antonio would forfeit a pound of his flesh if he cannot come up with the money at the appointed time.
let the forfeit
Be nominated for an equal pound
Of your fair flesh, to be cut off and taken
In what part of your body pleaseth me.
So, in Act III, Scene III, Shylock has come to claim his just due. In relation to his characterization as a dog with fangs, Shylock is reminding Antonio of their pact in Act 1 Scene III. He is really just using Antonio's metaphor of the Jewish 'dog' to remind the Christian lender that when promises are not kept, the consequences will be painful.