Does the degree of the victim's sentience correlate with the kamma associated with killing it? "One should not kill a living being,
  nor cause it to be killed,
  nor should one incite another to kill.
  Do not injure any being, either strong or weak, in the world.  
  
  Sutta Nipāta 2.396"


Is there more negative kamma associated with killing a biting insect than with killing a more sentient animal like a sparrow or mole?

For instance, do I incur more negative kamma by swatting a mosquito that is sucking my blood than if I kill a more sentient and less troublesome squirrel that is raiding my garden?
Yes, killing a human generates far more karma then crushing an ant. 
However the size of the seed does not determine the outcome of the seed. 

One teacher once noted that the karma of swatting a fly grows exponentially. 
That after a few days, especially if it is a repeated action, it can be grown to the size of the initial seed of killing a human. 

However the initial human killing seed grows similarly as fast. 

The thing is we have all these seeds or "karmic imprints" if you will, that are all maturing and ripening. Both good an bad, and they are coming in at a rate of around 60 imprints a second. 

I once let a mosquito eat its fill from my arm back when I was more seriously into Buddhism, the thought process was along the lines of sure, I have plenty of blood... eat up. The bite was magnificently itchy, and I will never do such again. 

Now I crush mosquitoes, I don't enjoy killing them, I don't seek it out, but if one is buzzing around in my apartment it is off to the bardo with it. 

However, squirrels raiding your garden, that is a slightly different scenario. Have you researched other options? Is there another way to protect your garden? It would be worth it to explore these questions from a karmic standpoint. 

Better to plant as few of those kinds of seeds as possible, or plant the opposite kind of seed... maybe out of compassion put out some food that squirrels eat and enjoy nearby, if the squirrel is hungry you will get the karma of feeding a being of lesser sentience. A full squirrel is less likely to raid your garden. 

Another thing to consider is the attachment to the garden, and the outcome of the harvest. If you lose one or two tomatoes, but harvest 12, really I'd say let the squirrel do its thing. I don't know the full extent of the raiding though, perhaps this squirrel ate all of your tomatoes. It still is not after your blood though, so there is that.