This paper reports a drug nanovehicle self-assembled from an amine-functionalized block copolymer poly(6,14-dimethyl-1,3,9,11-tetraoxa-6,14-diaza-cyclohexadecane-2,10-dione)-block-poly(1,3-dioxepan-2-one) (PADMC-b-PTeMC), which is prepared by controlable ring-opening block copolymerization attractively in a "one-shot feeding" pathway. The copolymers display high cell-biocompatibility with no apparent cytotoxicities detected in 293T and HeLa cells. Due to their amphiphilic nature, PADMC-b-PTeMC copolymers can self-assemble into nanosized micelles capable of loading anticancer drugs such as camptothecin (CPT) and doxorubicin (DOX). In particular, the outer PADMC shell endows the PADMC-b-PTeMC nanomicelles with pH-dependent control over the micellar morphology, cell uptake efficiency, and the drug release pattern. Confocal inspection reveals the remarkably enhanced cellular internalization of drug loaded micelles by cancerous HeLa cells at relatively lower pH 5.8 simulating the mildly acid microenvironment in tumors. Along with the acidity-triggered volume expansion of micelles, an accelerated CPT release in vitro occurs. The obtained results adumbrate the possibility of completely biodegradable PADMC-b-PTeMC as pH-sensitive drug carriers for tumor chemotherapy.