Two-dimensional (2D) materials with nanometer-size holes are promising systems for DNA sequencing, water purification, and molecule selection/separation. However, controllable creation of holes with uniform sizes and shapes is still a challenge, especially when the 2D material consists of several atomic layers as, e.g., MoS2, the archetypical transition metal dichalcogenide. We use analytical potential molecular dynamics simulations to study the response of 2D MoS2 to cluster irradiation. We model both freestanding and supported sheets and assess the amount of damage created in MoS2 by the impacts of noble gas clusters in a wide range of cluster energies and incident angles. We show that cluster irradiation can be used to produce uniform holes in 2D MoS2 with the diameter being dependent on cluster size and energy. Energetic clusters can also be used to displace sulfur atoms preferentially from either top or bottom layers of S atoms in MoS2 and also clean the surface of MoS2 sheets from adsorbents. Our results for MoS2, which should be relevant to other 2D transition metal dichalcogenides, suggest new routes toward cluster beam engineering of devices based on 2D inorganic materials.