Were there any bands from the states in the late 80s-early 90s playing a similar style to bands like Entombed, Carnage, Dismember, etc?

The older Autopsy stuff was a big influence on the Swedish scene.

But maybe an other hint:
Try to get everything from Ulcerous Phlegm. Best German Dödsmetall band together with older Fleshcrawl.
Also Hazael (Pol) - Thor CD. Very Swedish-sounding band from Poland back then. But only on this release.

Edit: typo cured. P.S.: add oldest Incantation from the US to the list. Especially their old EPs.

Give Gutted a try, their tone really reminds me of the "chainsaw" stuff. Great band from Ohio. Shame no one's ever heard of 'em. http://www.youtube.com/watch?v=XCNT2H1gG3s&feature=related

Mammoth Grinder's most recent MCD, Extinction of Humanity.

check out deteriorate - rotting in hell (1993), some of the greatest and rotten dm ever to come from the states in that period.
they had some carnage/dismember influences.

I remember hearing these guys on mp3.com back in the day. I had no idea they had a little cult following and that their shit went for an insane amount of money.

try funebrarum. get the split with interment, conjurations of the sepulchural. it's awesome.

Forgot: Deteriorot - In Ancient Beliefs CD. Totally Swedish/Finnish old-school massacre. The band released their first 7" in 1993. Though, the CD is a masterpiece.