Simultaneous wireless information and power transfer (SWIPT) is a major breakthrough in the field of low-power wireless information transmissions. In this paper, the secrecy performance of the SWIPT-enabled relay network with full-duplex destination-aided jamming is assessed, where both the power-splitting (PS) and time-switching (TS) schemes at the relay are considered with the linear and nonlinear energy harvesting models. The relay harvests energy from the confidential signal and artificial noise sent by the source and destination, respectively, and forwards the amplified signal to the destination, in the presence of an eavesdropper. The analytical closed-form expressions of the connection outage probability (COP), secrecy outage probability (SOP), and transmission outage probability (TOP) for PS- and TS-based schemes are derived, and the closed-form expression of the lower bound of ergodic secrecy capacity (ESC) is calculated. The asymptotic-form expressions of the COP, SOP, TOP, and ESC are further analyzed to capture the valuable information in the high SNR regime. Numerical results verify the correctness of analytical results, reveal the effects of the PS/TS ratio, and transmit the signal-to-noise ratio on secrecy performance.