How do you split a story that is too big to fit in a Sprint?

Short answer

Split vertically, so each slice goes end to end and delivers something demonstrable, using patterns such as workflow steps, business-rule variations, happy path first, and data or interface variants.

Treat this as a story splitting and refinement problem, not as a request to make tickets smaller. Good story splitting preserves a user-visible slice, keeps acceptance criteria testable, and gives refinement a sharper question to answer. Weak story splitting divides frontend, backend, and testing into separate tasks, which only creates partial work. Strong story splitting uses refinement to expose the real uncertainty, then splits around that uncertainty so each smaller story can still be reviewed and accepted. Story splitting is strongest when every slice still proves or disproves something useful.