The chemical investigation of Homotrigona apicalis propolis collected in Binh Dinh province, Vietnam, led to the isolation of nine compounds, including four sesquiterpenes: spathulenol (1), 1αH,5βH-aromandendrane-4β,10α-diol (2), 1β,6α-dihydroxy-4(15)-eudesmene (3), and 1βH,5βH-aromandendrane-4α,10β-diol (4); three triterpenes: acetyl oleanolic acid (5), 3α-hydroxytirucalla-8,24-dien-21-oic acid (6), and ursolic acid (7); and two xanthones: cochinchinone A (8) and α-mangostin (9). Sesquiterpens 1–4 and triterpene 6 were isolated for the first time from stingless bee propolis. Plants in the Cratoxylum and Aglaia genus were suggested as resin sources of the propolis sample. In the antibacterial activity evaluation, the EtOH extract only showed moderate activity on S. aureus, while the isolated compounds 7–9 showed good antibacterial activity, with IC50 values of 0.56 to 17.33 µg/mL. The EtOH extract displayed selective cytotoxicity against the A-549 cancer cell line, with IC50 values of 22.82 ± 0.86 µg/mL, and the xanthones 8 and 9 exhibited good activity against the KB, HepG-2, and A-549 cancer cell lines, with IC50 values ranging from 7.55 ± 0.25 µg/mL to 29.27 ± 2.07 µg/mL. The cytotoxic effects of xanthones 8 and 9 were determined by the inhibition of the EGFR and HER2 pathways using a molecular docking study. Compounds 8 and 9 displayed strong binding affinity with EFGR and HER2, with values of −9.3 to −9.9 kcal/mol. Compounds 5, 8, and 9 showed potential α-glucosidase inhibitory activities, which were further confirmed by computational studies. The binding energies of compounds 5, 8, and 9 were lower than that of arcabose.