Near a bandwidth-tuned Mott transition, the Fermi velocity v_F and quasiparticle residue Z of a metal often vanish. Here, we show that analogous phenomena emerge in twisted bilayer graphene (TBG) at integer fillings and can be captured by an emergent heavy-fermion framework within a projective active-band limit. Unlike models incorporating remote bands, our effective heavy-fermion description arises from mixed-valence Mott physics via decoupled charge and local-moment sectors. In the charge sector, active bands c(k) hybridize with an emergent orthogonal fermion ψ(k) to open a large Mott gap at |k| > k_* (k_* sets the momentum-patch size) and a quadratic band-touching semimetal near k=0 at neutrality (ν=0). The orthogonal fermion is a linear combination of the doublon and holon excitations and may be written as ψᵢ ∼ (δ nᶠᵢ+1/2)⁻¹ fᵢ. An emergent Kondo coupling J_K ∼ U (U is the local Hubbard interaction) between ψ and local moments ψ' frames the Mott transition as a Kondo screening transition, tuned by the twist angle θ. Away from the magic angle, a Kondo-screened heavy semimetal develops below T_K (the Kondo temperature) with vanishing Z. Introducing anti-Hund's coupling J_A generates an s-wave fully gapped or nematic, nodally gapped superconducting dome near the Mott boundary even at ν=0. At other integer fillings ν = ± 1, ± 2, increasing bandwidth first drives the small-gap Mott state into an intermediate quadratic band-touching semimetal before entering a heavy Fermi liquid with large Fermi surfaces. Our results establish a unified framework for emergent heavy fermion physics with both itinerant carriers and local moments from the f orbital.