The minor mode's hook is called both when activating and deactivating the minor mode, so how 'bout

(add-hook 'my-minor-mode-name-hook
          (lambda ()
            (if my-minor-mode-name
                (add-hook 'after-save-hook #'a-func-from-my-minor-mode nil 'local)
              (remove-hook 'after-save-hook #'a-func-from-my-minor-mode 'local))))

Note that your calls to add-hook are bothj global, so even though you only add to after-save-hook when the minor mode is called, this addition applies to all buffers. Maybe that was indeed what you wanted, but I assumed it's not in the above example code.

The minor mode's hook is called both when activating and deactivating the minor mode, so how 'bout

(add-hook 'my-minor-mode-name-hook
          (lambda ()
            (if my-minor-mode-name
                (add-hook 'after-save-hook #'a-func-from-my-minor-mode nil 'local)
              (remove-hook 'after-save-hook #'a-func-from-my-minor-mode 'local))))

Note that your calls to add-hook are both global, so even though you only add to after-save-hook when the minor mode is called, this addition applies to all buffers. Maybe that was indeed what you wanted, but I assumed it's not in the above example code.