Twisted bilayers of two-dimensional (2D) transition metal dichalcogenides are promising systems for achieving tunable quasicrystalline orders with emergent properties. The underpinning electronic structure and scattering processes in 2D quasicrystals with multiorbital dodecagonal replica bands have so far not been determined. Here, we utilize angle-resolved photoemission spectroscopy (ARPES) with micrometer spatial resolution to directly observe replica bands in 30^∘-twisted bilayer WSe₂. The symmetry and intensity distribution of the observed replicas are explained by interlayer Umklapp scattering from bottom to top WSe₂ layers. Our spectral function measurements are consistent with the presence of a van Hove singularity adjacent to the K-valleys, which underlines the possibility of inducing electronic reconstructions in bilayers with a large interlayer twist angle.