First review, so forgive me if I don't quite seem as knowledgeable as many others. Will certainly try and do my best to give my impressions

My heart sank as I watched Sadie running straight toward the tennis ball that was thrown.

A nice start but I would say "ran" rather than "running", or perhaps "rushed" considering Sadie appears to be a dog.

It accidentally hit a tree stump in the yard and bounded directly toward the road where an oncoming SUV was swerving this way and that; the driver texting on their cell phone

The sentence kind of drags on a little long so I would try splitting it into two sentences. Also you seem to use the present tense a bit oddly in this too.

As the ball bounced onto the road, I saw the exact second the driver realized what was transpiring on the road.

Get rid of the second "on the road". Ending with transpiring is better.

I picked her up and hurriedly carry her to my car

I assume you meant carried

to the nearest clinic and burst the doors open, Sadie in my arms.

Would add "I drove" or "I drove quickly" at the start of the sentence there.

She was currently living with a couple who ran an electronics repair boutique

No need for the currently. Something like "She was at the time" sounds better

It says “End of Life. Please return your PETronic Companion to the nearest PETronic Recycling Plant”.

Wasn't expecting that, but I did like the few clues you gave towards it. However with the way the rest of the piece went it did seem very sudden at the same time.

Overall its a decent idea, just could be phrased and such much better. The past and present tense mixups can be easily fixed, but ultimately I would suggest trying to find a way to make everything flow better :)