1998 Mazda 626 wires

The photo didn't load, but it sounds like you're describing an anti-lock brake wheel speed sensor. No other wires live close enough to the wheel to be cut by a tire. That wire will feel very rubbery and maybe even a little slimy. It is designed to withstand a real lot of flexing as the wheel moves up and down and turns. For that reason it is not practical to splice and repair it. The only way to get that wire is to buy the complete sensor. It would be called the "left front wheel speed sensor".

Yup; that's not a simple wheel speed sensor. Darn the bad luck.

The dealer's parts department will have a name for that harness and a part number, but there's almost no chance it is still available for a car that age. Also, all wiring harnesses are real expensive to buy new. Normally the only time you would get a new harness is when the car is still under warranty. For the disaster you have in your hand the typical repair is to splice in new pieces of wire and seal those splices with heat-shrink tubing. I just got done doing that in the same location on a smashed Dodge truck my friend is rebuilding.

Even buying a used harness from a salvage yard is not practical. There can be too many variations on identical models based on engine size, manual or automatic transmission, with or without air conditioning, cruise control, anti-lock brakes, etc. Even identical cars built a few months apart can have different harnesses. You'll also find that to remove a harness from a car in the salvage yard can take the better part of a day. Connectors are avoided and limited in number because they off a place for water to sneak in causing corrosion. For that reason that harness is going to go all around the engine compartment. No professional would try to replace the whole thing. It's just too involved.

What you might want to look at is the possibility of adding a few extra inches to each wire if that would let you locate the harness in a different spot to prevent this from happening again. When you're done and everything is working, you can bundle them up with electrical tape but then slip a piece of "convoluted tubing" over it to protect it. Normally I advise against electrical tape because it will unravel into a gooey mess on a hot day, but here you're not using it to seal a splice. It's just to keep all the wires together.

You can buy that convoluted tubing from any auto parts store, but this is something you CAN get from the salvage yard. It's the black plastic protective cover that was most likely on your harness to start with. It has a slit so you can spread it to slip over the wires. Every car in every salvage yard has a lot of that tubing. Just yank off a piece that's long enough and the right diameter.

You're welcome. I'm really tired now and can't keep my eyeballs open. I'll check back tomorrow to see if you made any progress.