Yes and no. Yes the passenger rail routes were absolutely slaughtered through the 50s, 60s and into the 70s (and occasionally even later see the withdrawal of Los Angeles to Las Vegas in 1997 when the Desert Wind was withdrawn or the Pioneer between Salt Lake and Seattle also in 1997) as car ownership rose and the interstate system developed followed by the spread of affordable air travel destroyed the market for train travel. But also it wasn't quite like Beeching because a lot of the railroads that withdrew their passenger services over that period were still operating their freight services (though at varying levels of profitability!) so a lot of lines so their passenger services withdrawn but remained open. That being said, however, I'd be willing to bet that the US has closed as much railway as the UK had at our greatest extent (probably several times over). They had a monumental amount of railway particularly in the east and still have a huge amount but somewhat more consolidated.
One of the more interesting features I've always found of the US system is the tiny railroads that still exist. Perhaps only operating a single branch line with a handful of locomotives. For instance
this outfit in Maryland that have 60 odd miles of track and ten locomotives. I believe there others that are even smaller (and others that are larger). Though of course they're nothing on the monsters like Union Pacific, CSX or BNSF (32,000, 21,000 and 32,000 miles of track each respectively).