Freestanding epitaxial metal nanoplates can be utilized as advanced three-dimensional platforms for various novel applications. Here we report the vapor-phase epitaxial growth of freestanding Pd, AuPd, and Au nanoplates on an a-cut sapphire substrate as well as the comprehensive study of their growth mechanisms and geometry tailoring. All as-grown Pd, AuPd, and Au nanoplates possess twin-free single crystallinity as well as are aligned three-dimensionally on the substrate with the same orientation. Interestingly, depending on their composition, they have the following three distinct geometries: trapezoid (Pd), hexagon (AuPd), or rhombus (Au). By analyzing the correlation of the geometry and orientation of the as-synthesized nanostructures, we reveal that all the nanoplates grow from square pyramidal seed crystals. The interfacial lattice mismatch between the bottom plane of the square pyramidal seeds and a-cut sapphire substrate increases in the following order: Pd < AuPd < Au. Consequently, the length of the interface between the bottom of the nanoplate and the substrate decreases in the following order: Pd > AuPd > Au; this leads to the resulting geometries of the synthesized nanoplates. Such a fundamental understanding of the growth mechanism would aid the growth of epitaxial metal nanostructures with the desired geometry, which is very attractive for building macroscale functional nanoarchitectures.