Two-dimensional (2D) semiconductors have emerged as exciting candidates for the development of low-power and multifunctional computing applications, thanks to their qualities such as layer-dependent band gap tunability, high carrier mobility, and excellent electrostatic control. Here, we explore a pair of 2D semiconductors with nearly broken-gap (Type-III-like) band alignment and demonstrate a highly gate-tunable p-MoTe₂/n-SnS₂ heterojunction with multifunctional behavior. Employing a dual-gated asymmetric device geometry, we unveil its functionality as both a forward and backward rectifying device. Moreover, we observe a highly gate-tunable negative differential resistance (NDR), with a gate-coupling efficiency of η ≃ 0.5 and a peak-to-valley ratio of ∼ 3 down to 150K. By employing density functional theory, we determine that the observed NDR is dominated by valence band-to-valence band tunneling, while additional interband tunneling contributions arise at higher bias. The combination of tunneling driven transport and gate controllability of NDR opens the pathway for realizing gate-tunable 2D material-based neuromorphic and energy-efficient electronics.