We have a 1 yr old male pug and when we first brought home our new puppy which is also a male but a mini dashund at first our pug did the stare then the stiff then suddenly it tried to hump the puppy. I don't know why and is there a way I can stop this from happening?

More than probably a dominance issue, your older dog is asserting himself as the 'boss' over the younger puppy.
How long have you had the new puppy?
Is the older male desexed?

When the older dog goes to hump the male get a spray bottle with cold water and give him a spritz in the face followed by a command (try and use a word other than 'no' as it tends to get overused and can confuse them). The water usually stops them in their tracks and is a good way to let him know that this behaviour is not on.

Also if the older dog hasn't been desexed now would be a good time to do so.

Can't add much to Shazamataz's post. Great advice there!

Another thing you can try is distraction. When he goes to hump, remove him from the puppy, and give him a toy or a bone and praise the acceptable behavior you are expecting.

No he isn't desexed and thank you for your advice and answering my question both of you have helped a lot thank you again.

No problem, and welcome to AMHD! :)