DicomBrowser (also here) will do that for you. Start the program, open the directory containing all of your files, and you'll get a listing on the left of the patient/study/series hierarchy. Select on the left just the series you want and use the Save operation (with "Write only selected files") to save those files to a new directory. (There's a small weirdness in the UI that you can't create a new directory at that point. I'll look into fixing that, but in the meantime you'll need to create a new directory yourself, using the command line or Explorer or the Finder or whatever makes sense on your computer.)