In Chapter Three, Victor says that he "began the creation of a human being." In order to achieve his goal, he requires "lifeless matter" so that he can "renew life where death had apparently devoted the body to corruption." In other words, he needs body parts, and so he must look in all of the places one might find those parts: the morgue (the "charnel houses" later referenced in chapter four), slaughter-houses, etc. He also says, in Chapter Three, that he "dabbled among the unhallowed damps of the grave [and] tortured the living animal to animate the lifeless clay." Thus, it sounds as though Victor actually did resort to digging up fresh graves in order to plunder the bodies buried there.
Importantly, it is in his "pursu[it] of nature to her hiding places" (the morgue, the grave, and other similar places that the average human eye avoids) that forces his "human nature to turn with loathing from [his] occupation" (chapter three).