Magnon current through mesoscopic ferro- or antiferromagnetic channel, sandwiched by bulk magnets, is investigated with a special attention to the effects of spin diluted sites introduced in the central scattering region of the channel. A scattering theory is developed to derive Landauer-type formula for magnon current which is applicable to both ferro- and anti-ferromagnetic channels. Making use of this formula, a series of numerical calculations of magnon transmission coefficient has been performed in the case of several typical configurations of spin diluted sites. It is shown that magnon transmission coefficient shows a series of sharp dips in the vicinity of bottom of magnon energy bands, reflecting the formation of resonance states in this energy region.