A man who was in the army during the Cold War told me that American soldiers would be stopped and executed if they were encountered by Soviet Patrols. I think he said this took place in Germany.
Over the course of the the Cold War there were several times when US military personnel were killed by Soviet military forces. There several US aircraft shot down by Soviet /Air Defense, many of which caused fatalities, these occurred when the planes either flew into Soviet air space or close to it.
There was also the matter of 64th Fighter Aviation Corps during the Korean War which had pilots of the USSR fly under the flag of the North Korea or the Chinese People's Liberation Army Air Force, which engaged UN forces (led by the US) in that conflict.
(see Xiaoming, Zhang "China, the Soviet Union, and the Korean War: From an Abortive Air War Plan to a Wartime Relationship". Journal of Conflict Studies. 2002.)
There has been (largely) anecdotally evidence of spetsnaz involvement in Vietnam but I have yet to find any source I would be willing to cite.
If you're asking, were any GIs killed in direct combat with Soviet troops, I don't know. But some GIs who had Russian origins and were liberated by the Soviet Army from German POW camps were later executed in the Soviet Union. http://articles.latimes.com/1992-11-12/news/mn-234_1_soviet-union