I think you're imagining a much larger asteroid than what is common. Oumuamua was at most a kilometer long and it was considered a large enough object. Most fly-through objects are much too small to be mined productively and also hold together well enough to act as shielding.

On top of that, the amount of stuff you'd need to mine it is also much larger than you might think. You need refining, production, maintenance, energy, and the rovers you're sending need precision tools to create precision installations. Think of the amount of mining that goes into making a single rocket on Earth, it requires several countries working together for every rocket launch, each with a power grid, an industrial base, a workforce, etc.

As a last point, if the object is going fast enough, staggering your operation so that it's not all in one go makes it so that everything needs to occur in a short timeframe, because the object is zipping out of the solar system pretty quick. By the time you see the object, calculate where it's going, get everything organized, you might have missed it.