Kirchberg announced quite a lot of years ago that $A\otimes_{\min{}} B$ is strongly purely infinite if $A$ is strongly purely infinite and $B$ is exact. Unfortunately, I don't think this result has ever been published.

Different results of the same nature are contained in [Blanchard, Etienne; Kirchberg, Eberhard Non-simple purely infinite C∗-algebras: the Hausdorff case. J. Funct. Anal. 207 (2004), no. 2, 461–513.]. For instance, Corollary 3.9 gives 8 different criteria for when $A\otimes_{\min{}} B$ is locally purely infinite, e.g. when $A$ is locally purely infinite and $B$ is exact.

In particular, if $A = B(\ell^2)/K(\ell^2)$ and $B = S\mathbb C$ (as suggested in the comments by S. Ge), then $A\otimes_{\min{}} B$ is locally purely infinite. By Proposition 5.1 and Theorem 5.8 from the before mentioned paper it follows that $A\otimes_{\min{}} B$ is strongly purely infinite.