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The method of magnetic particle imaging has a limited field of view due to physiological constraints. It is thus necessary to enlarge the field of view by a multi-patch approach in order to cover larger volumes. During reconstruction, truncation artifacts arise at the patches boundaries. We apply stochastic primal-dual hybrid gradient method to jointly reconstruct multi-patch magnetic particle images. We are thus able to apply a regularization, which takes into account neighborhood structures, not only on one patch but over all patches. Our experiments show that the quality of our reconstructions is significantly higher than the ones of reconstructions obtained by Kaczmarz method. Moreover, a joint reconstruction can considerably reduce the computational costs compared to multiple single-patch reconstructions.