Developing next‐generation antibiotics to eliminate multidrug‐resistant (MDR) bacteria/fungi and stubborn biofilms is challenging, because of the excessive use of currently available antibiotics. Herein, the fabrication of anti‐infection graphene quantum dots (GQDs) is reported, as a new class of topoisomerase (Topo) targeting nanoantibiotics, by modification of rich N‐heterocycles (pyridinic N) at edge sites. The membrane‐penetrating, nucleus‐localizing, DNA‐binding GQDs not only damage the cell walls/membranes of bacteria or fungi, but also inhibit DNA‐binding proteins, such as Topo I, thereby affecting DNA replication, transcription, and recombination. The obtained GQDs exhibit excellent broad‐spectrum antimicrobial activity against non‐MDR bacteria, MDR bacteria, endospores, and fungi. Beyond combating planktonic microorganisms, GQDs inhibit the formation of biofilms and can kill live bacteria inside biofilms. RNA‐seq further demonstrates the upregulation of riboflavin biosynthesis genes, DNA repair related genes, and transport proteins related genes in methicillin‐resistant S. aureus (MRSA) in response to the stress induced by GQDs. In vivo animal experiments indicate that the biocompatible GQDs promote wound healing in MRSA or C. albicans‐infected skin wound models. Thus, GQDs may be a promising antibacterial and antifungal candidate for clinical applications in treating infected wounds and eliminating already‐formed biofilms.