Clausuro comes from the verb clausurar, meaning to close, shut down, or adjourn. It's often used in a formal context, like closing a business or an event.
In this song, Christian Nodal uses it metaphorically and powerfully: "Será que su traición, le clausuro ya la memoria al corazón" (Perhaps your betrayal has already closed off the memory to my heart). He implies that the pain of betrayal has completely shut down his heart's ability to remember the past relationship, making it a unique and dramatic choice of word.
A woman shows up with a whole case against him: he was her lover, she says, he begged her to stay — "Que le supliqué que no se fuera de mi lado" (I begged her not to leave my side) — and sent her roses "de mes en mes" (month after month). His answer is just no. "Me va disculpar señora pero no recuerdo" (I'm sorry, ma'am, but I don't remember) — calling her "señora" instead of a name is the coldest word in the whole song. Then the chorus is nothing but questions thrown back at her: "¿Quién es usted? ¿De dónde ha salido?" (Who are you? Where did you come from?). By the end he's gone further than forgetting — "le clausuro ya la memoria al corazón" (I've already sealed my heart off from that memory) — like it was deliberate. Mariachi horns play under the whole thing, so the denial never even sounds angry.