ASTRI is a Flagship Project financed by the Italian Ministry of Education, University and Research, and led by INAF, the Italian National Institute of Astrophysics. Within this framework, INAF is currently developing an end-to-end prototype of a Small Size Telescope in a dual-mirror configuration (SST-2M) for the Cherenkov Telescope Array (CTA), scheduled to start data acquisition in 2014. Although the ASTRI SST-2M prototype is mainly a technological demonstrator, it will perform scientific observations of the Crab Nebula, Mrk 421 and Mrk 501 at E>1 TeV. A remarkable improvement in terms of performance could come from the operation, in 2016, of a SST-2M mini-array, composed of a few SST-2M telescopes to be placed at final CTA Southern Site. The SST mini-array will be able to study in great detail relatively bright sources (a few x 10E-12 erg/cm2/s at 10 TeV) with angular resolution of a few arcmin and energy resolution of about 10-15%. Thanks to the stereo approach, it will be possible to verify the wide field of view (FoV) performance through the detections of very high-energy showers with core located at a distance up to 500 m, to compare the mini-array performance with the Monte Carlo expectations by means of deep observations of selected targets, and to perform the first CTA science at the beginning of the mini-array operations. Prominent sources such as extreme blazars, nearby well-known BL Lac objects and radio-galaxies, galactic pulsar wind nebulae, supernovae remnants, micro-quasars, and the Galactic Center can be observed in a previously unexplored energy range, in order to investigate the electron acceleration and cooling, relativistic and non relativistic shocks, the search for cosmic-ray (CR) Pevatrons, the study of the CR propagation, and the impact of the extragalactic background light on the spectra of the sources.