In the U.S., no one disputes that secession is legal. The whole country was
founded by secession. It is, however, well-established by precedent that if any states do secede, the remaining states will then be able to launch a war of conquest against them, and re-annex their territory back into the union as a new entity with exactly the same name, borders, and government structure as before the secession occurred. If you want to secede, you must prepare to fight for it.
As of 1775, no English colony in North America had ever been independent. It had always been subject to the king of England. This was not sufficient reason for the colonists to remain loyal subjects of the crown.
The colonists took it upon their own initiative to secede from England. Any votes that may have been cast were taken mainly among those who wanted independence, and those who wished to remain loyal were likely not even informed that a vote was taking place. It isn't really there for a democratic mandate, but a means of gauging support among the uncommitted for any war that may follow.
In the ideal case, the result of the vote is strong enough that the war is a foregone conclusion, and it never actually happens. The WOPR concludes that the only way to win is not to play. Or it may be a means of the parent entity tactfully trying to shed a non-performant territory. Or it may be because people are genuinely trying to decide a course of action based on the will of the people. The U.S. territory of Puerto Rico, for instance, may one day hold a referendum to determine whether the island should apply for statehood, petition for independence, or remain in the status quo. It is likely that the remainder of the U.S. would honor the results of any such vote, though probably with the U.S. retaining sovereignty over any territory the military already directly controls.
It is not necessary for any national or international body to recognize the vote. It is purely for the secessionists, to determine if they could win a war if the parent entity invades after the split.
The secessionists don't have to pay any attention whatsoever to other regions with an equally strong or stronger case for secession.
If you are voting to secede, you don't care whether or not the vote is legal or binding. The explicit wording is regarding secession, but implicitly it is about whether people will take up arms for Catalonia, or at least not take up arms for Spain, if there is a war for independence. The percentages don't really matter, only the raw numbers. If 10000 people vote "yes", you know that there are potentially 10000 armed rebels out there, waiting for the signal to join the fight.
I think Spain is handling this in the worst possible manner, diplomatically. Viral videos of people getting beaten by police is only going to increase the number of people willing to fight to make it stop.