There's a complicated answer and a simple answer.
The simple answer is, "You can't."
WordPress requires three specific fields for every user - login (username), email, and password. Of those, login and email must be unique values.
Email is necessary for a user to retrieve access to the site if they have forgotten their password.
There are methods to remove username and replace it with email (or a value derived from the email), but they run into various problems. But there is no way to simply dump email as a required field. Not only is it required in the default registration form, the user profile update requires this field as well and there is no method of filtering it out. Period.
The complicated answer is based on the above. You would have to come up with a way to create a "spoof" value to fill in the email for the user. That would include validating your value to make sure it was unique, and then also making sure that you prevent any emails being sent to these values unintentionally. It would be problematic.