I see that Dead Alive have a lot of the ideas of Evil Dead such as exaggerated blood bath, monster puppets and stuff.
Is Evil Dead the pioneer of this type of funny horror or was there another major movie released before it?
I amended the question slightly to reflect the fact that Evil Dead was made 11 years before Brain Dead ('Dead Alive' in the US)
One might argue that Sam Raimi's 1981 classic, The Evil Dead, is indeed a pioneer in its own right as it paved the way for a multitude of amateur filmmakers to pick up their camcorders and create their own, ultra-gory, 'cabin-in-the-woods' movies. This resulted in many new filmmakers emerging from the carnage, Peter Jackson among them, whose equally gory Bad Taste was to be the first in a trio of over-the-top films (including Meet the Feebles and Dead Alive).
That said, Raimi himself was influenced by the films he watched while researching his target audience, low-budget foreign and domestic gore-fests that maintained a fast pace and were drenched in blood. Films such as H.G. Lewis' Blood Feast, Lucio Fulci's Zombie and even Romero's first two zombie classics, Night of the Living Dead and Dawn of the Dead. There are other influences in Raimi's breakthrough film, especially from Dario Argento, whose distinctive camera moves may have had an impression on Raimi, and we shouldn't forget the contribution of the films of Ray Harryhausen and The Three Stooges.
The Evil Dead is by no means the first 'funny' horror movie, as the two genres had gone hand in hand for many years beforehand, most notably in the output from Roger Corman.
As an aside, it looks like Joss Whedon is about to reinvent the genre all over again with his 2012 release, The Cabin in the Woods.
Peter Jackson has stated in an interview that he absolutely was influenced by people like George Romero and Sam Raimi: