Wait.
Do you want to sync 2 Google accounts to the phone? Or do you want to sync 2 gmail accounts to the phone? Those are totally different things.
I think you're talking about the second thing. So delete the work account from Settings/Accounts. Then delete the work contacts from the phone. Then add the work email address to your email app.
If you want it the other way, delete the personal account from Settings/Accounts, delete the personal contacts and add the personal email to your email app.
The Google account and the email account, even though they may be spelled exactly the same, are different accounts, depending on where in the phone you enter them.
If all you want is no work contacts, but everything else from work (and personal) in the phone, just go to Settings/Accounts and disable email sync, then delete all the work contacts.
Unfortunately, you can't check "all contacts" and delete them in one shot, but you could try turning off Contacts sync in the personal account, clearing data from the Contacts app (in Settings/Apps/Contacts), then turning contacts sync back on in Settings/Accounts in your personal account. But, only contacts that were entered as Google contacts get synced anyway. Contacts that were entered as Phone, Device or SIM contacts (the first line when adding a new contact, and the first - but it's read-only - line in editing a contact) do not get synced at all, so if the ones you don't want on the phone aren't entered as Google contacts aren't backed up somewhere else, deleting them from the phone deletes them from everywhere. Be careful.
But unless you want contacts, pictures, etc., synced to the Google cloud under your work account, the work account shouldn't be in Settings/Accounts to begin with. That account is only for syncing, not for email. (The email app picks it up when you're setting the phone up.) Keep your syncing accounts in Settings/Accounts and your email accounts in your email app.
Note: Being written while SpookDroid posted his post.