数学之分支代数拓扑学中，切除定理（Excision theorem）是关于相对同调的一个很有用的定理。给定拓扑空间 X 及其子空间 A 与 U 使得 U 也是 A 的子空间，此定理说在一定情形下，我们可将 U 从两个空间中切除使得空间偶 (X,A) 与 (X \ U,A \ U) 的相对同调群是同构的。这在奇异同调群的计算中很有用，在许多情形切除一个合适的子空间后更容易计算。或者，在许多情形，它使得可以应用归纳法。与同调中的长正合串行一起，我们可以导出计算同调群的另一个有用的工具迈耶-菲托里斯串行（Mayer–Vietoris sequence）。

In algebraic topology, a branch of mathematics, the excision theorem is a theorem about relative homology—given topological spaces X and subspaces A and U such that U is also a subspace of A, the theorem says that under certain circumstances, we can cut out (excise) U from both spaces such that the relative homologies of the pairs (X,A) and (X \ U,A \ U) are isomorphic. This assists in computation of singular homology groups, as sometimes after excising an appropriately chosen subspace we obtain something easier to compute. Or, in many cases, it allows the use of induction. Coupled with the long exact sequence in homology, one can derive another useful tool for the computation of homology groups, the Mayer–Vietoris sequence.