In this study, poly(isobutylene-alt-maleic anhydride) (PMA)-coated spinel ferrite (MFe2O4, where M = Fe, Co, Ni, or Zn) nanoparticles (NPs) were developed as carriers of the anticancer drugs doxorubicin (DOX) and methotrexate (MTX). Physical characterizations confirmed the formation of pure cubic structures (14–22 nm) with magnetic properties. Drug-loaded NPs exhibited tumor specificity with significantly higher (p < 0.005) drug release in an acidic environment (pH 5.5). The nanoparticles were highly colloidal (zeta potential = −35 to −26 mV) in deionized water, phosphate buffer saline (PBS), and sodium borate buffer (SBB). They showed elevated and dose-dependent cytotoxicity in vitro compared to free drug controls. The IC50 values ranged from 0.81 to 3.97 μg/mL for HepG2 and HT144 cells, whereas IC50 values for normal lymphocytes were 10 to 35 times higher (18.35–43.04 µg/mL). Cobalt ferrite (CFO) and zinc ferrite (ZFO) NPs were highly genotoxic (p < 0.05) in cancer cell lines. The nanoparticles caused cytotoxicity via oxidative stress, causing DNA damage and activation of p53-mediated cell cycle arrest (significantly elevated expression, p < 0.005, majorly G1 and G2/M arrest) and apoptosis. Cytotoxicity testing in 3D spheroids showed significant (p < 0.05) reduction in spheroid diameter and up to 74 ± 8.9% of cell death after two weeks. In addition, they also inhibited multidrug resistance (MDR) pump activity in both cell lines suggesting effectivity in MDR cancers. Among the tested MFe2O4 NPs, CFO nanocarriers were the most favorable for targeted cancer therapy due to excellent magnetic, colloidal, cytotoxic, and biocompatible aspects. However, detailed mechanistic, in vivo cytotoxicity, and magnetic-field-assisted studies are required to fully exploit these nanocarriers in therapeutic applications.