Toshiba Machine Co., whose illegal exports to the Soviet Union drew sharp criticism from the West last year, said Thursday it will cut its American operations in the face of restrictions on its U.S. exports.

"We understand it is only a matter of time now that the (U.S. trade) bill will be signed and take effect," said Hiroshi Yamaguchi, the company's senior spokesman. "So, whether we like it or not, we will have to trim down the U.S. unit sooner or later."If President Reagan signs the omnibus trade bill as expected, Toshiba Machine, which makes and sells machine tools, will be barred from exporting to the United States for three years.

The United States moved to penalize Toshiba Machine for selling milling machines to the Soviet Union that could be used to build quieter submarine propellers.