Can you have a male dog neutered
No, this is prohibited to do by yourself or to have a non Jew do it for you.
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.
See Nishmas Avraham (Even Ha-Ezer 5:9), citing from Rav S. Z. Auerbach; Shevet Ha-Levi (Vol. 6, no. 204); Har Zvi (Yoreh De’ah 23); Shevet Mi-Yehuudah 4:18.
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.