Since hyperthermophilic Archaea (HA) thrive in high-temperature environments, which accelerate the rates of deamination of base in DNA, their genomic stability is facing a severe challenge. Hypoxanthine (Hx) is one of the common deaminated bases in DNA. Generally, replication of Hx in DNA before repaired causes AT → GC mutation. Biochemical data have demonstrated that 3-methyladenine DNA glycosylase II (AlkA) and Family V uracil DNA glycosylase (UDG) from HA could excise Hx from DNA, thus triggering a base excision repair (BER) process for Hx repair. Besides, three endonucleases have been reported from HA: Endonuclease V (EndoV), Endonuclease Q (EndoQ), and Endonuclease NucS (EndoNucS), capable of cleaving Hx-containing DNA, thereby providing alternative pathways for Hx repair. Both EndoV and EndoQ could cleave one DNA strand with Hx, thus forming a nick and further initiating an alternative excision repair (AER) process for the follow-up repair. By comparison, EndoNucS cleaves both strands of Hx-containing DNA in a restriction endonuclease manner, thus producing a double-stranded break (DSB). This created DSB might be repaired by homologous recombination (HR) or by a combination activity of DNA polymerase (DNA pol), flap endonuclease 1 (FEN1), and DNA ligase (DNA lig). Herein, we reviewed the most recent advances in repair of Hx in DNA triggered by DNA glycosylases and endonucleases from HA, and proposed future research directions.