According to the BCTA, the Biewer is a relative of the Yorkshire Terrier, but has a distinct and separate Genetic makeup.
Although the Biewer Terrier is a relative to the Yorkshire Terrier it is evident that they are not the same breed. After two years of working with world renown geneticists at Mars Veterinary, we have been able to establish that the Biewer Terrier is a completely separate breed with a genetic make up, unique to the Biewer Terrier.
Biewer Terrier Club of America, Inc.
The BBCA only breeds Biewer to Biewer and not Biewer to Yorkie or Parti Yorkie. They also claim that the Biewer is a distinct breed that has Yorkshire Terrier in their history.
"Although the ancestry of the Biewer includes Yorkshire Terrier lines it is through select Biewer to Biewer breeding that has established the Biewer as a distinct breed."
Biewer Breed Club of America
So, from their point of view, breeding a Yorkie to Biewer would indeed result in a mixed breed.