As long as the meat is not fully thawed, that is it is kept below the temperature at which bacteria replicate you will be ok. Mince the meat with ice crystals present !
Mince itself should not be thawed and re- frozen but bigger portions are ok. This is because mincing will spread bacteria from the surface of the meat (aerobe's) through the mince and also incorporate air, so the bacteria can really get going during the re- freeze and next thaw period.
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