The use of grating based Talbot-Lau interferometry permits the acquisition of differential phase contrast (DPC) imaging with a conventional medical x-ray source and detector. However, due to the limited area of the gratings, limited area of the detector, or both, data truncation image artifacts are often observed in tomographic DPC acquisitions and reconstructions, such as tomosynthesis (limited-angle tomography). When data are truncated in the conventional x-ray absorption tomosynthesis imaging, a variety of methods have been developed to mitigate the truncation artifacts. However, the same strategies used to mitigate absorption truncation artifacts do not yield satisfactory reconstruction results in DPC tomosynthesis reconstruction. In this work,several new methods have been proposed to mitigate data truncation artifacts in a DPC tomosynthesis system. The proposed methods have been validated using experimental data of a mammography accreditation phantom, a bovine udder, as well as several human cadaver breast specimens using a bench-top DPC imaging system at our facility.