Deinking remains an important step in environmentally conscious manufacturing of paper. A novel method based on acoustic-coaxing-induced microcavitation is presented for deinking of xerographic ink from paper. Microcavitation evolves microimplosions which are effective in deinking. Acoustic coaxing is an acoustic mediation that enables one to control the onset, intensity, and evolution of acoustic microcavitation. Acoustic microcavitation is brought about by low-megahertz acoustic fields giving rise to micron-size bubbles that live a few microseconds. Liquid-borne microparticles when exposed to strong sound fields will not, ordinarily, cause any cavitation. However, if in addition to this sound field there exists even a very weak, high-frequency auxiliary acoustic field, cavitation by the microparticles is readily facilitated. This technique of facilitating cavitation is referred to as ``acoustic coaxing.'' Acoustic-coaxing methods for deinking are a chemical-free, environmentally responsible means of recycling paper. Here, initial experimental results are presented and the technique is elaborated upon in detail for easy implementation. Preliminary results indicate that the paper fibers are entirely undamaged, and the ink separation leaves them immaculately white. The microimplosions appear to occur preferentially at the ink sites.