When you set up Gmail on the mail software, did you use IMAP or POP3? If it was POP3, you can go ahead and clear out Gmail.
With IMAP, the local and server copies are linked, to allow you to keep several mail clients (computers, tablets, phones, etc) in sync.
With POP3, once messages are downloaded to your computer they no longer need to remain on the server. The Gmail POP3 setting basically pretends that it has removed messages from the server and keeps track of the requests made over POP3 so it only sends new messages.
Keep in mind that if you are using Gmail from a phone or tablet, anything you delete will be gone from those devices.
Also, if you aren't using Time Machine and/or an offsite backup service, I would absolutely do that before you trim down to a single local copy.
