CVS Health Corp.’s decision to stop covering Pfizer Inc.’s anti-impotence pill Viagra for many of its drug-benefit plan members is the latest example of the tough tactics some health-care managers are using to control rising drug costs.

CVS and rival Express Scripts Holding Co., which together dominate the U.S. market for administering drug-benefit plans for employers and insurers, are excluding more drugs from coverage if there are viable alternatives in attempts to squeeze greater price discounts from manufacturers. The...