Like all of them, ‘dash’ is the verb and ‘off’ is the preposition.  

‘Dash’ is something quick. Just dash off. 

I have to dash off for another meeting. Sorry, I can’t wait. I can’t talk to you, I’m in a hurry.

So they dash off. 

Or somebody’s trying to get some messages done before close of business on a Friday. He runs out to his secretary, 

Let’s just dash off a quick answer to these guys and then I can follow it up again on Monday.

‘To dash off’ means to do something very quickly. 

To dash off

1. to leave in a hurry

Sorry, I can’t talk to you. Do not dash off a reply in the heat of the moment.

2. to write something quickly without much effort

Do not dash off a reply in the heat of the moment. Take your time.