动手术 is a separable verb-object phrase. You can insert words between 动 and 手术: 动了手术 (had surgery), 动大手术 (have major surgery), 动过手术 (have had surgery before).
usage
Synonyms: 做手术 (zuò shǒushù) is more colloquial; 开刀 (kāidāo, literally 'open the knife') is informal. 动手术 is slightly more formal than 做手术.