Is preventing a neighbor from opening a blacksmith shop in a residential area, due to the harm and disturbance it causes, considered cutting off his livelihood?

What you did is permissible so long as it was done through legitimate means. Scholars have stipulated the prohibition of a neighbor causing harm to his neighbor. Your action is not considered cutting off his provision, for his provision is from his Lord, and Allah has guaranteed it for him. No human being can cut off a provision that Allah has decreed for His servant.