Likely you have the sending confirguration wrong.
Note: i dont use Mail for Ecchange - i run outlook.
But in any event, exchange is a modified IMAP protocol, and i believe Mail uses activ sync.
You have independent send and receive cpnfigurations it is perfectly possible to receive fine adn not be able to send.
Go to mail --> preferneces --> accounts
Open the exchange account.
Ender "accpunt information" click on "outgoing SMTP server" (SMTP is the protocol for outgoing mail - where your problem is).
Pull don the list and reveal "edit server list"
Now, find your Echange outgoing server and make sure that every single paramater - address, port, security, login, pasword etc is as needed. Ask you admin if needed.
Alternatively, delete your preferences file and start all over. You should nto lose exhcnage or IMAP mail nt he process. Thatis in users/you/library/preferences. To reveal the users/you/library folder requires that you go to "go" int he finder's menu bar at the top of the screen and press option. Magically, Library will appear.