FailedDev's answer is good, but can be improved. If you want to preserve the ascii equivalents, you need to normalize first:
String subjectString = "öäü";
subjectString = Normalizer.normalize(subjectString, Normalizer.Form.NFD);
String resultString = subjectString.replaceAll("[^\\x00-\\x7F]", "");
=> will produce "oau"
That way, characters like "öäü" will be mapped to "oau", which at least preserves some information. Without normalization, the resulting String will be blank.