The Cherenkov Telescope Array (CTA) is a worldwide project aimed at building the nextgeneration ground-based gamma-ray observatory. CTA will be composed of two arrays of telescopes of different sizes, one each in the Northern and Southern Hemispheres, to achieve a full sky-coverage and a ten-fold improvement in sensitivity over an unprecedented energy range extending from 20 GeV to 300 TeV. Within the CTA project, the Italian National Institute for Astrophysics (INAF) is eveloping an end-to-end prototype of the CTA Small-Size Telescopes with a dual-mirror (SST-2M) Schwarzschild-Couder configuration. The prototype, named ASTRI SST-2M, is located at the INAF “M.C. Fracastoro” observing station in Serra La Nave (Mt. Etna, Sicily) and is currently in the scientific and performance validation phase. A mini-array of (at least) nine ASTRI telescopes has been then proposed to be deployed at the Southern CTA site, by means of a collaborative effort carried out by institutes from Italy, Brazil, and South-Africa. The CTA/ASTRI team is developing an end-to-end software package for the reduction of the raw data acquired with both ASTRI SST-2M prototype and mini-array, with the aim of actively contributing to the global ongoing activities for the official data handling system of the CTA observatory. The group is also undertaking a massive Monte Carlo simulation data production using the detector Monte Carlo software adopted by the CTA consortium. Simulated data are being used to validate the simulation chain and evaluate the ASTRI SST-2M prototype and mini-array performance. Both activities are also carried out in the framework of the European H2020-ASTERICS (Astronomy ESFRI and Research Infrastructure Cluster) project. A data archiving system, for both ASTRI SST-2M prototype and mini-array, has been also developed by the CTA/ASTRI team, as a testbed for the scientific archive of CTA. The archive system provides the data access at different user levels and for different use cases, each one with a customized data organization. A dedicated framework to access, browse and download data produced by the ASTRI telescopes has been developed within a scientific gateway utility. In this contribution, we present the main components of the ASTRI data handling systems and report the status of their development.