The hat is a magical device, allowing the Saci to disappear, reappear and become invisible at will (though, his hat, even while invisible, seems to remain visible). It is also said to carry a foul odor, and those that would touch or pick it up will never be able to remove the stench from their person. The tradeoff is that he may grant a wish for the person upon taking hold of the hat.

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As stated above, the Saci is a trickster spirit, and with this is mind, is also known to be a shape-shifter. The Saci is said to take the form of a Matita Pereira, a breed of bird that’s said to sing melancholic songs. Aside from the above, other trickery the Saci is capable of ranges from dulling the needles of seamstresses, placing various curses unto objects and people, disturbing animal-life within the community, and causing milk to sour and eggs to become incapable of breaking.

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With the above in mind, certain methods can be taken to both assuage, and escape his wrath. One method to quell his offense is to cross a running river, if he too follows, he will lose all his powers. Another is to leave knots of rope lying around, like with many spirits, the Saci will almost have an OCD compulsion to try to untangle them. The Saci enjoys things like tobacco and cachaça, which can be used to get within his good favors. A method of not only completely disarming a Saci, but also capturing it is to throw a pair of rosary beads (with a sieve attached) into his twister, the Saci will then fall from his turbulence into what could be described as an agreeable state of mind. He can be persuaded into entering a dark green bottle, of which after he’s within, must be closed with a cork with a cross sign on the top. After being captured, it is said that he will grant wishes (the number is never specified), and afterwards (he’ll escape at some point), depending on the person’s treatment of him during his imprisonment, he will either become a powerful ally, or a formidable foe.
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Taken from Wikipedia:
“While some[who?] claim that the Saci myth originated in Europe in the 13th century such as the Monopod (creature), it probably derives from the Ŷaci-ŷaterê of Tupi-Guarani mythology, a magic one-legged child with bright red hair who would spell-bind people and break the forest's silence with his loud shouts and whistles. He was originally a creature of the night, and indeed the ŷaci (jaˈsi) means "Moon" in Old Tupi.
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This indigenous character was appropriated and transformed in the 18th century by the African slaves who had been brought in large numbers to Brazil. Farm slaves would tell Saci stories to amuse and frighten the children. In this process the creature became black, his red hair metamorphosed into a red cap, and, as the African elders who usually told the tales, he came to be always smoking his clay-and-reed pipe. His name mutated into various forms, such as Saci Taperê and Sá Pereira (a common Portuguese name), and eventually Saci Pererê.
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His red cap may have been inspired on the Phrygian cap at one time worn by Portuguese peasants. The Saci-Pererê concept shows some syncretism with Christian elements: he bolts away when faced with crosses, leaving behind a sulphurous smell — classical attributes of the devil in Christian folklore.
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The concepts of imprisoning a supernatural being in a bottle by a magically marked cork, and of forcing him to grant wishes in return of his liberty, have obvious parallels in the story of Aladdin from the Arabian Nights. This may be more than just a coincidence, since many slaves were Muslims and thus presumably familiar with the Arabian tales. Moreover, the occupation of parts of the Portuguese territory (namely in the south) by the Muslim Moors, between the years 711 and 1249, provides another possible path for Arabian influence on the Saci legend.”