Cannizzarite is a naturally occurring mineral formed by van der Waals (vdW) stacking of alternating layers of PbS-like and Bi2S3-like two-dimensional (2D) materials. Although the PbS-type and Bi2S3-type 2D material layers are structurally isotropic individually, the forced commensuration between these two types of layers while forming the heterostructure of cannizzarite induces strong structural anisotropy. Here we demonstrate the mechanical exfoliation of natural cannizzarite mineral to obtain thin vdW heterostructures of PbS-type and Bi2S3-type atomic layers. The structural anisotropy induced anisotropic optical properties of thin cannizzarite flakes are explored through angle-resolved polarized Raman scattering, linear dichroism, and polarization-dependent anisotropic third-harmonic generation. Our study establishes cannizzarite as a new natural vdW heterostructure-based 2D material with highly anisotropic optical properties for realizing polarization-sensitive linear and nonlinear photonic devices for future on-chip optical computing and optical information processing.