^

Ain't that one either. Though the year -95 could very well be the same.

Re: Does anyone know what movie is this? -HELP-
 

I'm willing to pay to the one who finds out what movie this is.

The Hunted?
Edit:sorry, I see now that was already mentioned...

Enter the Ninja (1981) is quite a bit older, but it features an American lead who defeats the villain by cutting off his head.

The Octagon (1985) is also pretty old, but Chuck Norris was the lead. In fact, it's worth looking through Norris' entire filmography because he made so many of these martial arts action films.

American Samurai (1992) is within range of the era you mentioned and David Bradley's filmography also should be looked over for the same reason as Norris.

Honestly, though, I'm wondering if perhaps you're conflating a few different films into one memory. Because American Ninja (1985) clearly has the cover you remember seeing and a lot of these types of films tended to include both American and Asian love interests (Big Trouble in Little China probably being the most famous example).

Re: Does anyone know what movie is this? -HELP-
 

Force of the ninja
American Warrior
Clash of the ninjas

They all have the American flag on the movie poster.

Re: Does anyone know what movie is this? -HELP-
 

It ain't anyone of those. Trust me, i search every movie you people keep posting.