I have no clue what your priest had in mind, but prior to 1970, missals used to have a section in the front called De Defectibus. One of the contingencies was what to do if a fly or spider fell in in the chalice. The answer was:
(a) drink it if you can, and it isn’t nauseous to you (a rare occurrence, I would think!)
(b) fish it out. Wash it over a chalice with wine. Then burn it and throw the ashes down the sacrarium.
The usual method of De Defectibus for disposing the Precious Blood was not to dilute It, since the proportion of water needed is somewhat uncertain, but to absorb It using a linen cloth, and wait for It to dry. Then burn the cloth and throw the ashes down the sacrarium.
Similar courses of action are prescribed with regard to impious rodents.
(To be honest, if a rodent did indeed materialize on the altar, I can’t imagine what most priests would do to catch it. Try smacking it with the paten, or the sacramentary? I guess this is one of the situations where the fans employed in some of the Eastern Rites would be in handy.)