Anti-satellite weapons have been demonstrated by the US, USSR, Russia, China, India, and if you stretch a bit Israel (they shot down a Houthi missile while it was above the Kármán line, the same system is probably capable of use as true anti-satellite weapon). Nobody has shot down anyone else's spy satellites, but it's not because it's impossible.
I think you might be misremembering the shoot-down of a U2 plane, which was also a U.S. spy plane operating around the same time.
> was
U2 is still in operation.
is there a reference for the USSR shooting an SR-71 down?
There is no reference for this, because it never happened.