This is a commonly-told but not actually true version of events. Here's what really happened between Jackson and the Cherokee case.
The background of the case is that the State of Georgia had enacted a law forbidding the settling of Cherokee territories by whites without a licence. A man by the name of Samuel Worcester, a missionary who helped establish the first Cherokee-language newspaper (the Cherokee Phoenix or ᏣᎳᎩ ᏧᎴᎯᏌᏅᎯ), protested against this law, saying that Georgia had no power to legislate what goes on in Cherokee territory, because the Cherokee Nation was sovereign over their own territory and not subject to the law of the State. The governor of Georgia ordered the arrest of Worcester and some other dissidents who refused to apply for a licence. He was brought before a Georgia court and stood trial, was convicted, and sentenced to four years' hard labour. Some of his fellow defendants accepted pardons from the governor, but Worcester refused the pardon in order to preserve his right to appeal his conviction.
The case was brought before the US Supreme Court, which ruled in the case of Worcester v. Georgia that the Cherokee Nation had sovereignty which the State of Georgia could not abridge, and that the law banning whites from settling Cherokee land was void. President Jackson expressed disdain over this ruling, and contemporary news thought he was unlikely to help the Supreme Court if it asked him to enforce its ruling. However, the Court never asked Jackson to send federal marshals to enforce the decision, so there was nothing for him to "violate".
Georgia state officials chose to ignore the ruling and refused to release Worcester from prison. His lawyers petitioned the new governor of Georgia to offer Worcester an unconditional pardon, but the governor refused, saying that the Supreme Court had overstepped its authority. Georgia officials decided to agitate for the federal government to impose a removal treaty against the Cherokees. Then, in an unrelated incident, South Carolina started a spat with the federal government by attempting to nullify a federal law that they didn't like, which caused the Jackson administration to change its tune towards Worcester's situation. His government dropped hints to the governor of Georgia that if Worcester (and another person similarly situated) were released, that the Jackson administration would arrange for a removal treaty to be imposed on the Cherokees. Worcester intended to continue pursuing his case before the federal courts but feared that doing so might provoke the government of Georgia to do something like attempt to secede or otherwise bring harm to the Cherokees. The governor and Worcester's legal representatives haggled over the wording of Worcester's petition for a pardon, and in the end, they were released the year after the Supreme Court's decision. Worcester gave up his case before the federal courts.
At the same time as this was happening, gold was discovered on Cherokee lands and the State of Georgia infringed on the Cherokees' sovereignty in other ways, including attempting to abolish the tribal government, trying to legislate away all of the Cherokees' land rights, and raffling off plots of Cherokee territory to white settlers.
In 1835 (three years after this ruling), a group of Cherokees not authorised by the Cherokee National Council or by their Principal Chief negotiated the Treaty of New Echota, agreeing on behalf the entire tribe to vacate their traditional homelands in exchange for five and a half million dollars and a reservation in Indian Territory (present-day Oklahoma). Despite the vast majority of Cherokee people opposing this treaty, its signatories having lacked the authority from the Cherokee council to negotiate it, and against the wishes of the Cherokee Principal Chief, the US Senate gave force to the treaty and President van Buren ordered the US Army to remove all Cherokees to Indian Territory in 1838.