Phase-contrast x-ray imaging is a promising improvement of conventional absorption-based mammography for early tumor detection. This potential has been demonstrated recently, utilizing structured gratings to obtain differential phase and dark-field scattering images. However, the inherently anisotropic imaging sensitivity of the proposed mono-directional approach yields only insufficient diagnostic information, and has low diagnostic sensitivity to highly oriented structures. To overcome these limitations, we present a two-directional x-ray phase-contrast mammography approach and demonstrate its advantages by applying it to a freshly dissected, cancerous mastectomy breast specimen. We illustrate that the two-directional scanning procedure overcomes the insufficient diagnostic value of a single scan, and reliably detects tumor structures, independently from their orientation within the breast. Our results indicate the indispensable diagnostic necessity and benefit of a multi-directional approach for x-ray phase-contrast mammography.