How standard relays mitigate the problem of electrical arc?
Relays at full capacity will spark a bit and generally wear out after a relatively small number of operations, perhaps 100,000 though some are rated for only 10,000-50,000 if the load is heavy and/or somewhat inductive or has a surge. They will, however, generally be extremely reliable during that lifetime- they tend to run quite cool and are robust against surges in voltage and current, unlike semiconductor switches. 

If no current is flowing through the contacts (or minimal) they can easily last for millions of operations. 

The relay contact material and the speed of opening/closing is what minimizes the arcing. Different metals and alloys are used for different purposes, optimized for the best possible life at reasonable cost.