您正在保存整个MIME对象（包括标头）。您需要做的是保存内容。

foreach (var attachment in message.Attachments) {
    using (var stream = File.Create ("fileName")) {
        if (attachment is MessagePart) {
            var part = (MessagePart) attachment;

            part.Message.WriteTo (stream);
        } else {
            var part = (MimePart) attachment;

            part.Content.DecodeTo (stream);
        }
    }
}