Redox and pH dual-responsive biodegradable micelles were developed based on poly(ethylene glycol)-SS-poly(2,4,6-trimethoxybenzylidene-pentaerythritol carbonate) (PEG-SS-PTMBPEC) copolymer and investigated for intracellular doxorubicin (DOX) release. PEG-SS-PTMBPEC copolymer with an Mn of 5.0–4.1 kg/mol formed micellar particles with an average diameter of 140 nm and a low polydispersity of 0.12. DOX was loaded into PEG-SS-PTMBPEC micelles with a decent drug loading content of 11.3 wt.%. The in vitro release studies showed that under physiological conditions only ca. 24.5% DOX was released from DOX-loaded micelles in 21 h. The release of DOX was significantly accelerated at pH 5.0 or in the presence of 10 mM glutathione (GSH) at pH 7.4, in which 62.8% and 74.3% of DOX was released, respectively, in 21 h. The drug release was further boosted under 10 mM GSH and pH 5.0 conditions, with 94.2% of DOX released in 10 h. Notably, DOX release was also facilitated by 2 or 4 h incubation at pH 5.0 and then at pH 7.4 with 10 mM GSH, which mimics the intracellular pathways of endocytosed micellar drugs. Confocal microscopy observation indicated that DOX was delivered and released into the nuclei of HeLa cells following 8 h incubation with DOX-loaded PEG-SS-PTMBPEC micelles, while DOX was mainly located in the cytoplasm for reduction-insensitive PEG-PTMBPEC controls. MTT assays revealed that DOX-loaded PEG-SS-PTMBPEC micelles had higher anti-tumor activity than reduction-insensitive controls, with low IC50 of 0.75 and 0.60 μg/mL for HeLa and RAW 264.7 cells, respectively, following 48 h incubation. PEG-SS-PTMBPEC micelles displayed low cytotoxicity up to a concentration of 1.0 mg/mL. These redox and pH dual-bioresponsive degradable micelles have appeared as a promising platform for targeted intracellular anticancer drug release.