By combining high-resolution transmission electron microscopy and associated analytical methods with first-principles calculations, we study the behavior of layered tin dichalcogenides under electron beam irradiation. We demonstrate that the controllable removal of chalcogen atoms due to electron irradiation, at both room and elevated temperatures, gives rise to transformations in the atomic structure of Sn-S and Sn-Se systems so that new phases with different properties can be induced. In particular, rhombohedral layered SnS2 and SnSe2 can be transformed via electron beam induced loss of chalcogen atoms into highly anisotropic orthorhombic layered SnS and SnSe. A striking dependence of the layer orientation of the resulting SnS - parallel to the layers of ultrathin SnS2 starting material, but slanted for transformations of thicker few-layer SnS2 - is rationalized by a transformation pathway in which vacancies group into ordered S-vacancy lines, which convert via a Sn2S3 intermediate to SnS. Absence of a stable Sn2Se3 intermediate precludes this pathway for the selenides, hence SnSe2 always transforms into basal plane oriented SnSe. Our results provide microscopic insights into the transformation mechanism and show how irradiation can be used to tune the properties of layered tin chalcogenides for applications in electronics, catalysis, or energy storage.