Stochastic reconstruction methods are of great value in microstructure modeling of porous media and numerical analyses researches. To achieve higher controllability and cope with different reconstruction tasks, a controllable generation method hybrid multiple-point statistics and sliced Wasserstein metric is presented, in which a controlled sampling strategy and a conditional reconstruction strategy are designed. The proposed method uses multipoint statistical information for characterization and combines sliced Wasserstein metric and gradient optimization for reconstruction. By purposeful sampling in the multipoint statistical information of reference image, the controlled sampling strategy can generate microstructures for a given phase volume fraction. With masks and conditional constraints, the conditional reconstruction strategy can reconstruct microstructures satisfying the given conditional data. Additionally, the proposed method can complete the above tasks with only a single data sample. Finally, visual comparison and statistical parameters are adopted to verify the effectiveness of the reconstruction results.