This work focused on characterizing the chemical constituents and evaluating the antioxidant and antimicrobial activities of the essential oils obtained from the fruit and leaves of Spondias mombin—a flowering plant of the Anacardiaceae family. Essential oils were extracted through steam distillation and characterized by gas chromatography-mass spectrometry. For the fruit essential oil, 35 compounds were obtained, and 25 compounds were identified in the leaf essential oil. The dominant compounds present in the fruit essential oil were (E)-ethyl cinnamate (14.06%) and benzyl benzoate (12.27%). Methyl salicylate (13.05%) and heptacosane (12.69%) were the abundant compounds in the leaf essential oil. The antioxidant activity of the essential oils was evaluated via phosphomolybdenum, hydrogen peroxide scavenging, 2, 2-diphenyl-1-picrylhydrazyl (DPPH) free radical scavenging, and thiobarbituric acid reactive substances (TBARS) assays. The total antioxidant capacity of fruit and leaf essential oils was 48.5 ± 0.7 μg/gAAE and 48.5 ± 0.7 μg/g AAE, respectively. The half maximal scavenging concentrations of the essential oils in the hydrogen peroxide; DPPH and TBARS assays ranged from 252.2 μg/mL to 2288 μg/mL. The antimicrobial activity of the essential oils was tested using broth dilution and disc diffusion assays against eight microorganisms. The essential oils exhibited broad-spectrum antimicrobial activity against the microorganisms with minimum inhibitory concentrations of 9.75–50 mg/mL. Also, the zones of inhibition of the oils ranged from 12 mm to 25 mm. The biofilm inhibitory activities of the oils were dose-dependent with BIC50 values of 42.49 ± 0.1 mg/mL and 97.34 ± 0.6 mg/mL for fruit and leaf essential oils, respectively. Molecular docking studies revealed that the antibiofilm action of the fruit and leaf essential oils could be due to inhibition of the quorum sensing protein, LasR. The results suggest a possible application of the oils as antioxidant and antimicrobial agents.