Studies have shown that nitrate (NO3−)-rich beetroot juice (BJ) supplementation improves endurance and high-intensity intermittent exercise. The dose–response effects on taekwondo following BJ supplementation are yet to be determined. This study aimed to investigate two acute doses of 400 mg of NO3− (BJ-400) and 800 mg of NO3− (BJ-800) on taekwondo-specific performance and cognitive function tests compared with a placebo (PL) and control (CON) conditions. Eight trained male taekwondo athletes (age: 20 ± 4 years, height: 180 ± 2 cm, body mass: 64.8 ± 4.0 kg) completed four experimental trials using a randomized, double-blind placebo-controlled design: BJ-400, BJ-800, PL, and CON. Participants consumed two doses of BJ-400 and BJ-800 or nitrate-depleted PL at 2.5 h prior to performing the Multiple Frequency Speed of Kick Test (FSKT). Countermovement jump (CMJ) was performed before the (FSKT) and PSTT, whereas cognitive function was assessed (via the Stroop test) before and after supplementation and 10 min following PSTT. Blood lactate was collected before the CMJ tests immediately and 3 min after the FSKT and PSST; rating of perceived exertion (RPE) was recorded during and after both specific taekwondo tests. No significant differences (p > 0.05), with moderate and large effect sizes, between conditions were observed for PSTT and FSKT performances. In addition, blood lactate, RPE, heart rate, and CMJ height were not significantly different among conditions (p > 0.05). However, after the PSTT test, cognitive function was higher in BJ-400 compared to other treatments (p < 0.05). It was concluded that acute intake of 400 and 800 mg of NO3− rich BJ reported a moderate to large effect size in anaerobic and aerobic; however, no statistical differences were found in taekwondo-specific performance.