Smote is the past tense form of the verb smite, which is most frequently used to mean "to strike sharply or heavily especially with the hand or with something held in the hand," or "to kill or severely injure by striking in such a way." Smite has two past participle forms (the form used with have and be), smitten and smote, as in "a villain who was smitten/smote by a sword." The former is more common.
It's an old-fashioned word that most modern English users encounter only in literature, and especially in older translations of the Bible, such as the King James Version:
And Moses lifted up his hand, and with his rod he smote the rock twice: and the water came out abundantly, and the congregation drank, and their beasts also.
— Numbers 20:11
So David prevailed over the Philistine with a sling and with a stone, and smote the Philistine, and slew him; but there was no sword in the hand of David.
— 1 Samuel 17:50
And the anger of the Lord was kindled against Uzza, and he smote him, because he put his hand to the ark: and there he died before God.
— 1 Chronicles 13:10
And immediately the angel of the Lord smote him, because he gave not God the glory: and he was eaten of worms, and gave up the ghost.
— Acts 12:23
The present tense form is found in the same kinds of contexts:
But if any man hate his neighbour, and lie in wait for him, and rise up against him, and smite him mortally that he die, and fleeth into one of these cities: Then the elders of his city shall send and fetch him thence, and deliver him into the hand of the avenger of blood, that he may die.
— Deuteronomy 19:11-12
Smite comes from an Old English word meaning “to smear or defile,” and the meanings of the word continued to have negative connotations as the word moved from Old English to Middle English and on to Early Modern English. Most of its meanings over the centuries have had to do with striking, hitting, injuring, punishing, or afflicting someone. The following is a very partial list of the kinds of things people were getting smitten with in books in the first half of the 17th century: leprosy, death, the plague, blindness, fear, sorrow, remorse, a most stinking and vile disease, ulcers, boils, the sword, fiery darts from heaven, the pox, barrenness, angels, God’s displeasure/hand/scourges/rod/terrible thunderbolts/wrath.
It was clearly not a very good time to be smitten. But in the middle of the 17th century there began to be signs that getting smitten might not be so bad after all. The word smitten, that past participle form of smite, was taking on new meaning:
Me-thinks from utmost Inns of Court I see
Young Amorists smitten with Bellesa's look
Caught by the Gills, and fastned to your Book.
—Walter Montagu, The Shepheard’s Paradise, 1659
But smitten with love on sweet Jenny he gaz'd,
and beg'd on his knees that she there would remain….
—(Anon.), The Amorous Gallant, 1655
Around 1650, smitten began to refer not simply to being struck, but to being struck with affection or longing. This sense existed for hundreds of years alongside all the senses one would rather avoid. But the fact that smite had dissimilar meanings does not seem to have confused many people. (We have no evidence, for example, of an exchange like this: “I found myself smitten.” “Wait… do you mean you’re in love, or do you mean that God’s displeasure has rained fiery darts of leprosy from heaven upon you? Very confused here.”)
By the late 18th century, smitten was being used as a full-blown adjective with the meaning "deeply affected with or struck by strong feelings of attraction, affection, or infatuation." It continued (and continues still) to function as a past participle of smite, as does smote. Smote is, however, most often used as the past tense of smite.
In summary, we'll close with a short guide to the 21st century forms of smite:
You plan on inflicting dire and retributive punishment on someone: “I will smite you.”
A man has inflicted dire and retributive punishment on you: “He smote me.”
You are in love (or you have experienced a plague of frogs): “I have been smitten.”