What is the Biblical source for the mandate (and amount) to tithe?

The word tithe means tenth. It is first used when Abraham encountered Melchizedek, who was a priest of God, and who blessed Abraham. In return Abraham gave him a tenth of all he had. See Genesis 14:18-20.

Later the tithe is prominent in the law of Moses. In all that God commanded the Israelites to do, he commanded a tenth of their increase to be given back to him. The tithe was meant to support the priests, who depended on the tithe for their livelihood.

And all the tithe of the land, whether of the seed of the land, or of the fruit of the tree, is the LORD's: it is holy unto the LORD (Lev 27:30 KJV).

But the tithes of the children of Israel, which they offer as an heave offering unto the LORD, I have given to the Levites to inherit: therefore I have said unto them, Among the children of Israel they shall have no inheritance (Num. 18:24 KJV).

There is also great promise made for those who give a tenth:

Will a man rob God? Yet ye have robbed me. But ye say, Wherein have we robbed thee? In tithes and offerings. Ye are cursed with a curse: for ye have robbed me, even this whole nation.

Bring ye all the tithes into the storehouse, that there may be meat in mine house, and prove me now herewith, saith the LORD of hosts, if I will not open you the windows of heaven, and pour you out a blessing, that there shall not be room enough to receive it. And I will rebuke the devourer for your sakes, and he shall not destroy the fruits of your ground; neither shall your vine cast her fruit before the time in the field, saith the LORD of hosts. And all nations shall call you blessed: for ye shall be a delightsome land, saith the LORD of hosts (Malachi 3:8-12 KJV).

Tithing is not a command in the New Testament, but that does not invalidate the promise of blessing. The principle is that we should acknowledge that everything already belongs to God. Giving a tenth back to him shows that you recognize your role as a steward of God's things, and not your own.