Homology of 4-manifold minus a small ball

Question

Let $X$ be a simply connected compact 4-manifold without boundary. We know that $H_4(X)=\mathbb Z$. Intuitively, I can see why removing a small (open) 4-ball $D^4$ would kill the top homology, but I'm having trouble proving it. I tried using excision and Mayer--Vietoris, but neither seemed very helpful. One source I found said that it is "because" $X'=X-D^4$ has boundary $\partial X'=S^3$, but I don't see how that helps.