Don't know which country you're from but yeah, it sucks to end up in a situation like this.
If I were you, I'd approach whoever received this fake email and honestly explain to him the situation. You'll have to make it clear that this hate mail did not, in fact originate from anyone that work in the organization/company you are from. Also explain to them how Tor work.
BTW, you mentioned that your 'email id' was hacked by a third party, but you didn't specify what kind of email system you're using. Assuming you are using a commercial email system, that indicate either your password is weak or your computer that handles email was compromised by malware. If you still have access to the mailbox, either change password immediately or cancel it to prevent further exploits from happening. If you're using your organization's own email system, then your IT guy need to patch it up immediately.
If all else fails, you'll have no choice but cooperating with law enforcement. If you can identify the computer(s) that were compromised by hacker, make sure you prevent anyone from accessing them, you never know hacker might leave trails on them that may exonerate you and your company's name!