These are great tips @lismox! My family also takes advantage of subscribe and save through Chewy for my pups food.
Something that has really saved us is pet insurance. It does require a monthly payment, but has saved us so much in the long run with our accident prone Lab. We do a $200 annual deductible with 90% reimbursement. The only thing it hasn't covered for us are annual vaccines and the cost of the visit itself.
I would also look into wellness plans through your vet. These typically cover the vaccines and visits, plus they offer discounts on medications/services. Again it was an upfront, annual cost but in the long run we got our money back on the cost of visits alone.
Thanks for the reminder about pet insurance @Ashlee. I don't have it currently, but it might be something to look into, especially since we have 3 cats!