A high-intensity proton beam accelerated in the J-PARC main ring (MR) is slowly extracted using third integer resonance and delivered to the experimental hall. A critical issue in slow extraction (SX) is beam loss during the extraction process. An achromatic dynamic bump scheme has provided extremely high extraction efficiency. Beam instability during the debunching process has been suppressed through sophisticated RF manipulations. Spill feedback and transverse RF techniques have improved the time structure of the extracted beam. A beam power of 92 kW was achieved in combination with a diffuser shadowing technique. The 8 GeV bunched slow extraction tests for the muon-to-electron conversion experiment (COMET Phase-I) have been successfully conducted. This paper provides an overview of J-PARC SX and related hardware in Part I and reports on the achieved SX beam performance in Part II.