But Article II, Section 3 of the Constitution provides in part that the president and, by extension, the Executive Branch, "shall take Care that the Laws be faithfully executed".
The Supreme Court has no resources with which to enforce its decisions. Therefore, another way of reversing Supreme Court decisions is for the Executive Branch to refuse to enforce them.
Conventional wisdom has it that that happened in response to the Court's decision in the 1832 case of Worcester v. Georgia. But, in the opinion of many observers, that point of view oversimplifies the story.
The case is often described along these lines: The Supreme Court, still led by Marshall, prohibited President Andrew Jackson from forcibly moving Indians from southeastern states to the western territories. Jackson refused to obey, saying "John Marshall has made his decision; now let him enforce it!" That's an inaccurate description, but it's not 180 degrees opposite to the truth.
Samuel Worcester was a white missionary working among the Cherokee tribe in Georgia. In violation of state law, Worcester had not secured Georgia's permission to live among the Cherokees. He was convicted in state court, and appealed that decision to the federal courts on the basis that a treaty between the U.S. and the Cherokee tribe has the same status in federal law as a treaty with, say, Britain or France.
The Supreme Court sided with Worcester. Marshall's opinion read in part:
The Cherokee Nation, then, is a distinct community, occupying its own territory, with boundaries accurately described, in which the laws of Georgia can have no force, and which the citizens of Georgia have no right to enter but with the assent of the Cherokees themselves or in conformity with treaties and with the acts of Congress. The whole intercourse between the United States and this nation is, by our Constitution and laws, vested in the government of the United States.
In a narrow sense, the Court's decision was obeyed. Georgia released Worcester from prison.
But the Cherokee people were eventually forcibly removed from Georgia under the Jackson Administration's policy of "Indian Removal". That seems to run counter to the Supreme Court's interpretation of the Cherokee treaties. But the removal was supported by new treaties, albeit of questionable validity, so that apparently was the legal basis that was not effectively challenged in the courts.
So, did Georgia and the federal Executive Branch defy the Court? Sort of.
What was Jackson's actual reaction to the Worcester decision?:
The decision of the Supreme court has fell still born, and they find that it cannot coerce Georgia to yield to its mandate.
It lacks the drama of "let him enforce it!", so it's understandable that that apparently apocryphal version is still widely quoted.