In this paper, we study two externally forced magnetic reconnection events near NOAA active region 12494 for their current sheet (CS) formation. In both events, small-scale reconnection happened between mini-filaments and other preexisting magnetic fields. Initially, mini-filaments underwent obvious non-radial rotating motion due to their loss of equilibrium. With their clockwise/anti-clockwise rotation, the axial fluxes of the mini-filaments slowly came to squeeze the anti-parallel ambient fields, leading to an X-shaped structure. As the squeezing effect strengthened, CS regions gradually formed and grew in length, with a temperature around 1.8 MK. Afterward, clear cusp regions, plasma heating (similar to 5 MK), and newborn magnetic structures came to be in sequence. Finally, mini-filaments erupted in a complex fashion due to the involvement of external reconnection. Based on the multiwavelength imaging observations, the apparent thickness/length, temperature/emission of the CS regions and their related plasma flows are carefully analyzed. Their reconnection rates are roughly estimated as 0.01-0.06 and 0.01-0.02. In particular, a chain of high-speed plasmoid ejections was detected along with a set of the reconnected field lines in Event1, implying the onset of tearing-mode instability inside its CS region. These observations indicate that non-radial rotating motion of filaments can serve as external flows to drive reconnection, and also provide a basic scenario of CS formation within small-scale magnetic reconnetion processes.