The issue of the cut-off splicing of an additional fiber-reinforced polymer (FRP) bar in the near-surface mounted (NSM) technique for reinforced concrete (RC) beam strengthening exposed dominantly to bending is insufficiently investigated. A possible solution of this issue is a new proposed technique: a double-strap joint. It implies the widening of the groove at the cut-off location and the symmetrical installing of additional supplements of FRP reinforcement. In this research, beam strength has been determined for the following cases: additional NSM FRP reinforcement without a cut-off, with a cut-off, and without overlapping, and with different lengths of splice overlapping. A nonlinear analysis based on the finite element method (FEM) has been applied. The length of the cut-off splice of the additional FRP reinforcement with glass fibers (GFRP) was 20Ø, 40Ø, and 60Ø. The validation of the numerical model and a comparison of the results were conducted by using the authors’ experiments. It has been shown that, in the case of a cut-off of NSM GFRP bars, a significant loss in strengthening efficiency occurs, and that, with an increase in the overlapping length, this loss decreases. An overlapping length of 60Ø provides full strengthening. An efficiency assessment was carried out via the use of a parametric study, varying the FRP bar material type and its diameter for a constant splicing length.