These words all have a very similar meaning and are really interchangeable. They all are verbs that mean “make something good again that was damaged or worn out.” The choice of which word to use is really idiomatic. The best way to think about their use is to think about the kinds of nouns that would receive their action:
Reconstruct - a building, a road (for example, after an earthquake)
Restore - a painting, the paint on furniture or a car, damaged files on your computer
Repair – the engine in your car, a machine that was broken (a washing machine), a musical instrument
Mend – clothing that was torn, a heart that was broken due to a bad relationship