This letter investigates the performance of rate-splitting multiple access (RSMA)-assisted terahertz (THz)-based short-packet communication (SPC) networks to serve multi-users simultaneously. Considering the impact of imperfect successive interference cancellation (SIC), an approximate closed-form expression for the users’ block-error rate (BLER) is derived. Based on this, an asymptotic behavior of users’ BLER is carried out to reveal some useful insights, which include diversity and coding gains, the trade-off between the BLER constraint and the system transmit power/user communication range, and power allocation (PA) and blocklength design for the intended message streams. Moreover, the exact and asymptotic analyses for the users’ ergodic rate are also performed. Numerical results validate the theoretical analyses and it is shown that: 1) the BLER can be improved by optimizing the common PA coefficient; 2) the trade-off between the system BLER demand and the achieved ergodic rate can be enhanced by increasing the number of antennas at the source; and 3) RSMA has a superior ergodic sum rate over its space division, orthogonal, and non-orthogonal multiple access counterparts.