To contort something is to bend or twist it out of its original shape. Faces are often said to contort with one particular emotion or another.
In general contort refers to something that is fairly adaptable and can return to its previous shape. A face, after it has contorted with rage, for example, will return to its normal expression (unless you've done something really bad.). If you bend or twist your sister's doll, you "break it" rather than "contort it."