Such groups exist even over $S = \mathrm{Spec} \mathbb{Z}$. See, for instance, Eg. 6.2 of http://math.stanford.edu/~conrad/papers/redgpZ.pdf or other places of that paper. If $\mathscr{G}$ there had a maximal torus over $\mathbb{Z}$, then that maximal torus would be split, contradicting anisotropy of $G_{\mathbb{R}}$.

Counterexamples exist even over $S = \mathrm{Spec} \mathbb{Z}$. See, for instance, Lemma 1.1 and Example 6.2 of http://math.stanford.edu/~conrad/papers/redgpZ.pdf or other places of that paper. If $\mathscr{G}$ in Example 6.2 there had a maximal torus over $\mathbb{Z}$, then that maximal torus would be split, contradicting the anisotropy of $G_{\mathbb{R}}$.