Is there any heter to spade a dog, she has already had several pups?
There is a prohibition against neutering an animal, whether male or female. This prohibition applies even after the animal has had litters. This is certainly true for instances in which the sterilization is desired only for the sake of convenience. However, indirect methods of causing infertility might be permitted.
Sources: See Shulchan Aruch, Even Ha’ezer 5:11 (some maintain that sterilization of a female is only a rabbnic prohibition); Rabbi Moshe Feinstein, Iggros Moshe, Even Ha’ezer IV, 34; For an overview of the issue, see Rabbi Joseph Ozarowski, “Tubal Ligation and Jewish Law: An overview,” Journal of Halacha and Contemporary Society VII, pp. 42-52.
For modern methods of potentially permitted sterilization, see McRae, G.I., et.al. “Long-term Reversible Suppression of Estrus in Bitches with Nafarelin Acetate, a Potent LHRH agonist,” Journal of Reproductive Fertility,(1985) 74 389-397; and Olson, P.N., et.al. “A Need for Sterilization, Contraception, and Obortifacients: Unwanted Pets Part IV. Potential Methods of Controlling Reproduction,” Compendium of Continuing Education, Vol. 8, No. 5, May 1986, 303-307.