Stochastic uncertainty widely exists in practical engineering problems, and the coupling and propagation of uncertainty can easily lead to large fluctuations in the response of engineering products or even failure. Therefore, it is necessary to quantify, propagate and control stochastic uncertainty. The traditional uncertainty propagation method mainly starts from the performance function, and realizes uncertainty propagation with higher efficiency or accuracy by approximating or expanding the performance function. This paper develops a relatively novel random uncertainty propagation method. Starting from the input random variable, the Gaussian mixture model is used to split the distribution of the input variable into the sum of several Gaussian distributions with small variances. Firstly, in the case of multivariate input random variables, the K-value criterion is proposed, which can simultaneously consider the influence of performance function nonlinearity and input random variable covariance on the response PDF. Secondly, the direction of splitting is selected according to the size of the K-value, which splits the input random variable into a Gaussian mixture model along the selected direction. Thirdly, the individual components of the Gaussian mixture model are propagated one by one to obtain the output response PDF. Finally, the convergence criterion based on Shannon entropy is used to ensure the accuracy of uncertainty propagation.  The effectiveness of the method is verified using the numerical examples.