Let's see...  I honestly have never heard that.  But I doubt that it is true, because I only use my tarot deck when the need arises, which can be as long as 6-7 months in between.  And all three of my dogs and my cat are in good health.  So honestly, I think it was just coincidence.  I'm sorry your pets died.  If you feel your tarot deck is causing these problems, I suggest either cleansing it, or getting a new one, an animal based tarot might be just the thing you need and might break your bad luck streak.