The ASTRI Mini-Array (ASTRI MA) is a project led by the Italian "Istituto Nazionale di Astrofisica" (INAF) to build and operate a next-generation imaging atmospheric Cherenkov telescope observatory for ground-based gamma-ray astronomy in the energy range between 1 TeV and 100 TeV and beyond. It will be composed of nine small-sized (~4 meter in diameter) and large field-of-view (~10 degrees) double-mirror telescopes equipped with silicon photo-multiplier cameras. The full array will be operational within the next few years at the Observatorio del Teide (Tenerife, Spain). It will allow deep observations of the galactic and extragalactic sky with a significantly improved performance at multi-TeV energies compared to current arrays of Cherenkov telescopes, providing a fully functional complement to both present- and next-generation gamma-ray observatories in the Northern Hemisphere. In order to assess the performance of the system and to generate suitable Instrument Response Functions for high-level scientific studies, detailed high-statistic Monte Carlo simulations were generated and subsequently processed with A-SciSoft (ASTRI Scientific Software), the scientific software package of the ASTRI Project. In this contribution, we describe the main features of both the simulation and data processing chains and present the performance of the ASTRI MA achieved with the aforementioned Monte Carlo simulations.