I shall quote a previous answer of mine to Henry the VIII ushered in the Reformation, all because he wanted a divorce. Since he went through all this effort, why didn't he just divorce or demote Ann Boleyn instead of executing her?

Well, to start, he didn't usher in the Reformation "all because he wanted a divorce". From an earlier answer of mine:

For one thing, Henry believed that if he were with the right woman and God blessed their union, a son would be granted to them. Remember that a major factor in his stated reasoning for divorcing Catherine of Aragon (really, annulling their marriage - having it retroactively undone) was that he claimed to believe she and his brother had consummated their marriage, and that therefore he had sinned by marrying her and was being punished with daughters, stillbirths, and children who died young. If he corrected his error, then God would be like, "Now we're good!" and provide a healthy, male heir to the throne

There is so much room for historians to argue about the level of impact different factors had in the English reformation - political divisions between England and Spain/the HRE, the pope's intractability over granting the annulment, actual theological issues, Henry's desire for Anne and Anne's refusal to be a mistress, the lack of a viable male heir - but it's about a lot more than simply a plan to get a divorce.

But I'm here today to talk about the second part of your question, because queens are more my jam than the religious-political backdrop of the Reformation. The major reason that Anne Boleyn was executed is that she was accused and convicted of adultery, and adultery from the queen was treason. And treason was punished with execution.

Anne was accused of having slept with her own brother, George, Viscount of Rochford, as well as Sir William Brereton, Sir Francis Weston, Sir Henry Norris, and Mark Smeaton; Brereton, Weston, and Norris were all members of Henry's privy chamber (his inner circle), and Smeaton was a musician at court. Even worse, she was accused of having conspired at Henry's death in order to marry one of them. The times and places of the alleged adulterous incidents didn't really work out - she was accused of sleeping with Norris a month after she gave birth to Elizabeth, for instance, and of sleeping with Brereton at Hampton Court Palace a few months later when the whole court was at Greenwich - but that didn't matter. Men of the period were horrified and terrified of the specter of the adulterous wife, who debased their right to have sex with her by sharing it with others, and who put the paternity of all her children in doubt. Perhaps even worse, she put them into the ridiculed position of the cuckold, a man who couldn't control his wife. it was far more important to the all-male court to denounce the adultery and make it clear to other women (and the men who might sleep with them) that they would face high penalties for it. Henry was feeling all of this and the jury knew what he wanted them to do.

But, okay. Let's adjust the question to "why didn't Henry divorce/demote her before then?"

Eric Ives argues that much of the machinery of the trial for adultery was put into motion by Thomas Cromwell (Henry's highly influential officer) without Henry's knowledge, as a way to force Anne's fall from grace. Cromwell and Anne were very opposed in politics, and it would have been to Cromwell's benefit to remove her ability to influence Henry and public opinion. The Spanish ambassador, Eustace Chapuys, claimed that Cromwell told him Anne was out of favor even as Henry was insisting on her being recognized by foreign courts as the rightful queen. Cromwell then told Henry that she was an adulteress, probably capitalizing on her miscarriage just a few months earlier of a fetus said to be male, and tortured Mark Smeaton into a confession, and then Anne was very suddenly arrested. (After her arrest, she was unwittingly pumped for incriminating information that was then inflated and used to create compelling specific charges.) Under this theory, Henry simply wasn't that interested in getting a new queen before that point. He was beginning to pay attention to Jane Seymour, but there was no indication that it was serious enough to result in another rupture and a new queen until he turned from Anne - Ives describes his attentions as "courtly" practically all the way up to Anne's trial.

Other than all this talk of adultery, there were really no grounds for a divorce or annulment. The question of an engagement (and/or sexual contact) between Anne and Henry Percy, which could have derailed Anne's marriage to Henry, had been dealt with several years before they actually wed. It would have also been difficult to persuade Henry to declare that his marriage to Anne was invalid because his personal annulment of his marriage to Katherine was invalid, as that would give the impression of going back on all of his rebellion against the pope and his belief in his own supremacy. Her marriage was declared annulled only shortly before her execution, and we don't have the documents that say exactly why, and it was done to take Elizabeth (now illegitimate) out of the line of succession, to eradicate Anne from history. By that point, the justification wasn't really important.