Constrained by increasing deficits and decreasing ridership, the Amtrak board of directors put the brakes yesterday on America's already faltering love affair with the train by cutting five well-known passenger train routes.

Two of the routes cut were the National Limited from New York to Kansas City, with one stop a day in Washington, and the Hilltopper, which connects Boston and Washington to the Ashland, Ky., area. Saved was the Blue Ridge commuter train from Washington through suburban Maryland to Martinsburg, W. Va.

The board, acting unanimously, yesterday merely complied with a congressional mandate to cut about 16 percent of the least-used miles and consequently improve service and save millions of dollars in federal subsidies. Amtrak, formed in 1971 from a number of unprofitable railroads, was meant to do just that.

In the mandate, in legislation being nailed down by both houses, for a train to operate under the cut-back system it must have a minimum of 150 passengers per train mile and losses not exceeding seven cents a passenger mile. Amtrak used the latest rider figures to determine which routes would meet the congressional criteria.

"The board was severely restricted by Congress' mandate," Amtrak President Alan S. Boyd said. "They laid out the criteria, and we just had to compile the information."

The system must be cut back by Oct. 1.

"The end of September is going to be the end of those trains," Boyd said.

The fate of two other Washington routes, the Shenandoah from Washington to Cincinnati and the Cardinal from Washington to Chicago, are in limbo pending resolution of conflicts in the House and Senate versions. Conferees from both houses are expected to hammer out those and other details in about two weeks, an Amtrak spokesman said.

Two Washington routes spared are the Broadway Limited connecting New York, Washington and Chicago and the Montrealer from Washington to Montreal.

As the golden era of the locomotive has passed, so will a number of well-known train routes. In addition to the two Washington routes, they are the North Coast Hiawatha from Chicago to Seattle; the Floridian from Chicago to Florida, and the Lone Star from Chicago to Houston. Despite its losses, Chicago remains the hub of railroading, an Amtrak spokesman said.

Following Congress' criteria, the National Limited had 103 projected passengers per train mile and a projected loss per passenger mile of 7.5 cents for fiscal 1980 while comparable figures for the Hilltopper are 29 passengers and 25 cents.

Several years ago, the Hilltopper was ordered reinstated by Congress after its route, which traveled through the West Virginia hometown of Senate Majority leader Robert C. Byrd, was cut.

Amtrak's commuter trains won an 18-month reprieve, however, to give state and local governments time to figure out how to finance their operation.

President Carter originally wanted the system reduced by 43 percent but later backed down when rail usage zoomed with the appearance of the energy shortage.