A \(d\)-dimensional stochastic differential equation of the form \[ dX_t=b(X_t)dt+\sigma (X_t)dw_t,\quad t\geq 0,\tag{1} \] with an initial condition \(X_0=x\in R^d\) is considered where \(w_t\) is a \(d_1\)-dimensional Wiener process, \(d_1\geq d\), \(b\) and \(\sigma \) denote a \(d\)-dimensional locally bounded Borel function and bounded continuous nondegenerate \(d\times d_1\)-matrix function, respectively, defined on \(R^d\). Under weak recurrency assumptions, polynomial bounds for the coefficients of \(\beta \)-mixing are established; in particular, the speed of (polynomial) convergence of probability laws of solutions of the equation (1) to the invariant measure is estimated. The method of proof is based on direct evaluation of the moments and certain functionals of hitting times of the solutions to (1).