I answered this question initially a while back (here), but I thought I would expound on it further for my upcoming Q&A in the parish bulletin. Here's what I wrote:
Q: Did Jesus break the Law of Moses by not stoning the woman caught in adultery?
Great question! The incident you are referring to is found in Jn 8:3-11. The Pharisees catch an adulterous woman and bring her to Jesus to see what He will do. You may want to open your bible to this passage so that you can have it on hand as I discuss what is happening here.
Now, at first glance, it may appear that Jesus did break the Law of Moses. After all, the Law stated that anyone who commits adultery must be stoned to death (cf. Lev 20:10; Deut 22:20-22), yet Jesus prevented this woman from being stoned. However, the truth is this: Jesus did not break the Law here, He fulfilled it.
First, we must keep in mind that the truest justice comes not when the Law is enforced by those who are themselves transgressors of it (as all mankind are), but when it is enforced by He who is sinless, who is in no way a transgressor of the Law of God (cf. Heb 4:15; 1 Pet 2:22; 1 Jn 3:5). When Jesus said to the Pharisees, “Let him who is without sin cast the first stone,” He basically revealed to the crowd that He is the ultimate Judge, not the Pharisees (or anyone else, for that matter).
Once He established that, He went on to enforce the Law when He said to the woman, “Go and sin no more.” After all, the purpose or spirit of this particular law (which the Pharisees so often neglected) was to impress upon Israel the gravity of the sin of adultery. Jesus acknowledged this when He told the woman to never do it again.
Finally, note that stoning the woman would have meant the condemnation of both the sin and the woman. She would have died in sin and suffered total separation from God. But, Jesus came to condemn sin, not sinners. He came to save what was lost, not to lose it (cf. Lk 19:10; Jn 12:47; 18:9). So, by preventing the stoning while at the same time commanding the woman to “Go and sin no more,” Jesus condemns the sin but saves the sinner. In this way, He is both Just and Merciful, and He brings about the fulfillment of the law in question.