This can't be done with mysqldump directly. However, you can create a temporary table or a view that does not contain the data in question, and then dump the resulting data. In the case of a view, I think you'll have to use
INTO OUTFILE rather than mysqldump to get the data you want, but using a view instead of a temporary table has the advantage of not taking up any extra space in the DBMS.
The other option is to create a parser for the file to strip the fields you don't want. To put it mildly, this can get complicated very quickly, that is if you want to create a parser that's robust in the face of multibyte characters, escaped string separators, etc., etc. But for the trivial or one-time-use case, it may still be a valid option.