A new mixed ligand–silver(i) complex of formula [Ag(tpp)₂(p-Hbza)] (1) (p-HbzaH = 4-hydroxybenzoic acid and tpp = triphenylphosphine) has been synthesized and characterized by elemental analysis, mp, vibrational spectroscopy (mid- and far-FT-IR), ¹H-NMR, UV-vis, ESI-MS spectroscopic techniques and X-ray crystallography. Complex 1 and the already known mixed ligand–silver(i) complexes of formulae [Ag(tpp)₂(salH)] (2) (salH₂ = salicylic acid or 2-hydroxy-benzoic acid) and {[Ag(tpp)₃(asp)](dmf)} (3) (aspH = o-acetylsalicylic acid) were used for the clarification of the cytostatic activity mechanism. Thus, 1–3 were tested for their in vitro cytotoxic activity against leiomyosarcoma (LMS) and human breast adenocarcinoma (MCF-7) cells with trypan blue and Thiazolyl Blue Tetrazolium Bromide (MTT) assays. For both cell lines, complexes 1–3 were found to be more active than cisplatin. Due to the morphology of the LMS cells after incubation with 1–3, the type of cell death was evaluated by flow cytometry assay and DNA fragmentation. The results show that LMS cells undergo programmed cell death (apoptosis). DNA binding tests indicate the ability of complexes 1–3 to modify the activity of the cells. The binding constants of 1–3 towards calf-thymus DNA (CT-DNA) ((27.7 ± 7.9) × 10⁴ (1), (13.3 ± 6.5) × 10⁴ (2) and (11 ± 2.8) × 10⁴ (3) M⁻¹) indicate strong interaction. Moreover, the influence of complexes 1–3 on the catalytic peroxidation of linoleic acid to hydroperoxylinoleic acid by the enzyme lipoxygenase (LOX) was kinetically studied. Finally, docking studies on DNA binding interactions were performed.