How do I remove an exchange mail account?

I am having the same issue. I no longer work with the company and would like to remove the exchange account from the phone. The "delete account" option is not available when you go in to settings -> mail,contacts, calendars.

iPhone 5s - iOS 8.3

If you go to Settings>Mail, Contacts, Calendars, do you see the Account in question? If so, can you select it? If you can select it, you are saying that you do not have the option to delete it? Do you have an Exchange profile installed on your device from the former employer?

Is this your personal phone or a company phone? If a company phone and they set it up for you, you may need their IT people to remove it. Companies do have the ability to make it impossible for the account to be removed without proper authority and authentication.

Personal phone, had my company email installed... i no longer work with the company so going to their IT team is not a possibility.

Correct, when I select it there is no option to delete. I believe I do have an exchange profile installed from my former employer.

You will need to delete that profile, since it appears that is what is preventing you from removing the account. Just because you no longer work for them, if they installed a profile on your device as a condition of your employment, once you severed your employment with them, they would need to remove the profile. You have the ability to check with them about this if such a profile exists. I would give them a phone call if you have difficulty locating and deleting the profile. It may require you to restore the iPhone as new.

Try settings -> general -> profile if there is a profile, try removing that by clicking on it. if you can remove it, then after that, the option to remove the account should appear (or it may disappear anyway with the profile).