Dig it with electric mining tools, heat it with a solar furnace, and ship it with electric trucks?

Maybe, but that's not how it's done today, and it's not the sort of thing you change overnight.

Complicating matters is the fly ash component of modern concrete. Fly ash can replace 50% or more of the portland cement in concrete. Fly ash is a byproduct of burning coal. So when you replace the coal plants with solar arrays, you need to create even more portland cement than you would need to if you were burning coal (and using the subsequent fly ash in your concrete.)

I've read that kilns used to produce the clinker are often fueled by burning waste like used car tires.

Wikipedia speaks to it a bit:

https://en.wikipedia.org/wiki/Cement_kiln#Alternative_fuels