Five pH-responsive $alkyne$-poly(2-aminoethyl methacrylate)-$graft$-poly($L$-glutamic acid) ($alkyne$-PAMA-$g$-PLGA) comb copolymers were synthesized through the ring-opening polymerization (ROP) of ${gamma}$-benzyl-$L$-glutamate $N$-carboxyanhydride (BLG NCA) and the subsequent deprotection of benzyl group from BLG unit. The chemical structures of copolymers were confirmed by proton nuclear magnetic resonance spectra ($^1H$ NMR) and Fourier transform infrared spectroscopy (FTIR). The pyrene-probe-based fluorescence technique and transmission electron microscopy (TEM) measurements revealed that the comb copolymers could spontaneously self-assemble into micellar or vesicular nanoparticles in phosphate buffered saline (PBS) at pH 7.4. Doxorubicin (DOX), an anthracycline anticancer drug, was loaded into nanoparticles as a model anticancer drug. The $in$ $vitro$ release results showed that the release behaviors could be altered by adjusting the composition of the comb copolymer and pH of the release medium. $In$ $vitro$ methyl thiazolyl tetrazolium (MTT) assays demonstrated that the copolymers were biocompatible, and DOX-loaded nanoparticles showed effective inhibition of cellular proliferation. Hemolysis tests indicated that the copolymers were also hemocompatible, and that the presence of the copolymers could reduce the hemolysis ratio (HR) of the DOX significantly. In addition, the comb copolymers could be modified through versatile Cu(I)-catalyzed "click chemistry" between the terminal alkyne group and azide-modified functional agents. These properties indicate that the pH-responsive clickable comb copolymers are promising candidates for multifunctional nanocarriers in cancer diagnosis and therapy.