Answer
The proposed decay process does not conserve spin angular momentum.
Work Step by Step
The $\Xi^-$ has spin $\frac{1}{2}$
The $\pi^-$ has spin $0$
The neutron $n$ has spin $\frac{1}{2}$
The $K^-$ has spin $0$
The proton $p$ has spin $\frac{1}{2}$
The left side of the proposed decay process can have net spin angular momentum $\pm \frac{1}{2}$ while the right side of the proposed decay process can have net spin angular momentum $0$ or $\pm 1$
Therefore, the proposed decay process does not conserve spin angular momentum.
