Blue Jays do NOT eat the meat of birds and mammals. Yes, they WILL eat the eggs of other birds if they cannot find enough food, but they prefer seeds, seedlings (watch your gardens!), berries and small fruits, and insects (they are great for mosquito control!). In my 28 years of caring for, and watching wild birds I have found that Blue Jays get along great wih other song birds, especially doves and robins. They can get a little aggressive in a food shortage, but that is typical of any species. Blue Jays DO hate mice, and may attack them on sight, noone knows why. Hey, natural pest control!

Scub Jays, on the other hand, will attempt to DOMINATE any territory they set up shop in. I’m currently having difficulty with a family of them myself. They will run off all other birds, attack squirrels, dive bomb your cat, make alot of racket at 4 AM, and be a general nuisance, and yes, they will attempt to kill anything that doesn’t comply with their territorial demands, even YOU. There are only four ways to get rid of Scrub Jays, and no way is 100% effective.
1: Attract as many Hummingbirds as possible to your yard. The two species hate each other and Hummingbirds will not hesitate to attack Scrub Jays (and crows!) especially if they can get a buddy to help. However, it goes both ways, so only employ this method if you are prepared for a full-out war to take place in your backyard and you are willing to deal with the casualties. This method is both difficult and costly, however. It is always difficult to attract large numbers of Hummingbirds, especially since thier numbers are dropping due to our stupidity, and it is a time-consuming method. Remember, you CANNOT allow Hummingbird food (or sugar water) to remain in your feeder for longer than two days, one day in very hot weather. AND, you must throughly clean your feeders EACH time you refill them. Why? because the slightest bit of mold build-up will kill your little friends when they drink. The black mold causes their tongues to swell to the point that they cannot feed, and Hummingbirds must feed several times a day to live. Repeated exposure will cause the tongue to swell to the point of cutting off their airway, which in a Hummingbird leads to guaranteed death in around 40 seconds. Most people either don’t know, or don’t bother with keeping their feeders clean, and this mold can form in less than 48 hours after sun exposure to the food. The whole time you think your doing a nice thing for your feathered friends, you maybe killing them instead.
2: Remove ALL sources of food from your yard. Scrub Jays are lazy birds and will only set up shop in places where they is a ready supply of seed, nuts, insects, or small animals. Remove all birdseed, squrriel food, spray for outdoor insects, and try to convince your neighbors to do the same until the Scrubs have moved on to greener pastures.
3: Soak birdseed, sunflower seeds, and peanuts in a solution made from mouse/rat poison. Get some DECON mouse poison from your local supermarket or home improvement store. Mix four tablespoons of it into 12 ounces of water. Mix well and allow to dissolve as much as possible, leaving it overnight if you must. Make multiple 12 ounce batches if you wish. Pour into a large bowel, mix in seed and peanuts and allow to soak overnight. Drain the next day and allow seed to dry on a layer of papertowels. When seed/peanuts are all dry, dump em in a plastic bowl or whatever and place outside on your porch table or anywhere else Scrub Jays like to feed in your yard. Repeat as required. In a few days, you’ll have dead Scrubs. WARNING: Be mindful of other wildlife when employing this method.
4: ‘Ye Olde BB/Pellet Gun. Best used in combination with peanuts as bait. In the country I find a scoped Ruger 10/22 works best. More range and greater accuracy. although I HATE to kill things, sometimes you gotta.

Happy Bird Watching!