i = string.offsetByCodePoints(i, -1);
  shaveBytes -= computeByteLength(string.codePointAt(i), encoding);

A small assumption is each encoding has all chars at byte boundaries. In other words, ComputeByteLength for a string input is just the sum of ComputeByteLength for all contained codepoints.

Assuming that computeByteLength can accept an int instead of a char, you get this.

public static String limitStringByBytes(String string, int maxBytes, String encoding) {
   if(string == null)
      return "";
   int i = string.length();
   int shaveBytes = computeByteLength(string,encoding) - maxBytes;
   while ( shaveBytes > 0 && i > 0 ) {
      i = string.offsetByCodePoints(i, -1);
      shaveBytes -= computeByteLength(string.codePointAt(i), encoding);
   }
   if( i <= 0 )
      return "";
   else
      return string.substring(0, i);
}