What is a printing process where the artist cuts away an image from a soft synthetic material.?

The printing process you’re referring to is known as linocut. In this technique, the artist carves an image into a soft linoleum block, removing the areas that will not be printed. Ink is then applied to the raised surface, and the block is pressed onto paper to create the final print. This method allows for bold, graphic images and is popular among printmakers.