Yes. Take $f\in O_K$ a uniformizing element of some prime $\mathfrak p$. Consider the hyperelliptic curve defined by the equation 
$$y^2=x^{2g+1}+f.$$ 
Then this curve doesn't have semi-stable reduction at $\mathfrak p$.  In fact, this equation defines a proper regular model of the curve over the localization $O_{K, \mathfrak p}$ and this model is minimal because its closed fiber is irreducible (defined by $y^2=x^{2g+1}$), and it is not semi-stable. If the curve had semi-stable reduction, the minimal regular model would also be semi-stable. Further, this curve is far from being semi-stable because its Jacobian has purely additive reduction at $\mathfrak p$.