As novel states of quantum matter, quantum spin Hall (QSH) and quantum anomalous Hall (QAH) states have attracted considerable interest in condensed matter and materials science communities. Recently, a monolayer of the naturally occurring mineral jacutingaite (Pt2HgSe3), was theoretically proposed to be a large-gap QSH insulator and experimentally confirmed. Here, based on first-principles calculations and tight-binding modeling, we demonstrate QSH to QAH phase transition in jacutingaite by chemical functionalization with chalogen. We show that two-dimensional (2D) chalogenated jacutingaite, Pt2HgSe3-X (X = S, Se, Te), is ferromagnetic with Curie temperature up to 316 K, and it exhibits QAH effect with chiral edge states inside a sizeable topological gap. The physical mechanism lies in the adsorption induced transformation of the original Kane-Mele model into an effective four-band model involving (p(x), p(y)) orbitals on a hexagonal lattice, so that the topological gap size can be controlled by spin-orbit coupling strength of the chalogen (0.28 eV for Pt2HgSe3-Te). These results not only show the promise of functionalization in orbital-engineering of 2D functional structures, but also provide an ideal and practical platform for achieving exotic topological phases for dissipationless transport and quantum computing.