The industrial processing of crude propolis generates residues. Essential oils (EOs) from propolis residues could be a potential source of natural bioactive compounds to replace antibiotics and synthetic antioxidants in pig production. In this study, we determined the antibacterial/antioxidant activity of EOs from crude organic propolis (EOP) and from propolis residues, moist residue (EOMR), and dried residue (EODR), and further elucidated their chemical composition. The EOs were extracted by hydrodistillation, and their volatile profile was tentatively identified by GC-MS. All EOs had an antibacterial effect on Escherichia coli and Lactobacillus plantarum as they caused disturbances on the growth kinetics of both bacteria. However, EODR had more selective antibacterial activity, as it caused a higher reduction in the maximal culture density (D) of E. coli (86.7%) than L. plantarum (46.9%). EODR exhibited mild antioxidant activity, whereas EOMR showed the highest antioxidant activity (ABTS = 0.90 µmol TE/mg, FRAP = 463.97 µmol Fe2+/mg) and phenolic content (58.41 mg GAE/g). Each EO had a different chemical composition, but α-pinene and β-pinene were the major compounds detected in the samples. Interestingly, specific minor compounds were detected in a higher relative amount in EOMR and EODR as compared to EOP. Therefore, these minor compounds are most likely responsible for the biological properties of EODR and EOMR. Collectively, our findings suggest that the EOs from propolis residues could be resourcefully used as natural antibacterial/antioxidant additives in pig production.