Only two of the four gospels, Matthew and Mark, mention Jesus being offered something to drink before being placed on the cross. Matthew 27:33 - 34 refers to this drink as wine mixed with gall, while Mark calls it wine and myrrh (Mark 15:23). Both Biblical verses refer to the same thing.
They came to a place called Golgotha, which means, 'The Place of the Skull.' There they offered Jesus wine mixed with a bitter substance (most translations have "gall"); but after tasting it, he would not drink it (Matthew 27:33 - 34).
When Was He Offered It?
Jesus was offered a wine and gall mix to drink just before 9 a.m. on Wednesday, April 5 in 30 A.D. He was offered the drink after arriving at Golgotha, but before the Romans nailed him to the cross and cast lots for his clothes.
The English word "gall," in the New Testament, comes from the Greek word chole (Strong's Concordance #G5521) which literally means poison. All the Old Testament verses that use this word (Lamentations 3:5, 3:19, Jeremiah 8:14, 9:15, 23:15 and so on) have a common definition of something that tastes bitter and is (many times) poisonous.
Uses
A mixture of wine and gall was commonly given to criminals before their execution in order to ease some of their suffering. As an ex-chemistry teacher, I taught that all poisons are bitter but acids are sour. Christ likely refused this drink knowing that its bitter taste meant it was more of a poison than a painkiller.
Jesus did not want to die from poisoning or have his senses numbed while on the cross. He knew that He had to shed his blood in order for Him to become the supreme sacrifice for the sins of all man, and He refused to take the easy way out of it.
Fulfilling Prophecy
The offering of this concoction by the Romans, however, was a fulfillment of a prophecy given by King David. While in the depths of a painful trial David cried out to the Eternal that his enemies gave him only something bitter to quench his thirst.
You have known my reproach, and my shame, and my dishonor; my enemies are all before You.
Reproach has broken my heart, and I am full of heaviness; and I looked for sympathy, but there was none; and for comforters, but I found none. They also gave Me gall for My food; and in My thirst they gave Me vinegar to drink (Psalm 69:19 - 21, HBFV).
Although refusing what the Roman guards initially offered him when he arrived at Golgotha, Jesus later did take some sour wine when he was on the cross (Matthew 27:48). This was acceptable for his thirst because, though it had a sour taste, he knew that it was not poisonous.
Our Savior Dies
After hanging and suffering on the cross for six hours, in the heat of the day, Matthew 27 and John 19 tell us what ultimately ended the life of man's Savior. His suffering quickly ended after a Roman soldier plunged a spear into His side, causing both blood and water to come out of the wound. This stab also fulfilled Bible prophecy (Zechariah 12:10).
. . . Then another took a spear and thrust it into His side, and out came water and blood. And after crying out again with a loud voice, Jesus yielded up His spirit (Matthew 27:49 - 50, HBFV).
Many ancient manuscripts contain a statement at the end of Matthew 27:49, not included in the KJV Bible, which mentions Jesus having his side pierced by a spear BEFORE he died. Modern Biblical translations like those by James Moffatt (1926) and Ferrar Fenton (1903), as well as footnotes in the NASB and NLT Bibles record this fact.
The Roman soldiers who normally would break a person's legs to hasten death did not need to do so for Jesus (John 19:31 - 33). This was because the piercing he received, while still barely alive, caused him to bleed and end his life quicker. Pilate's surprise that Christ died so fast (Mark 15:44 - 45), in spite of not having broken legs (Pilate required a centurion to attest to his death) further supports this conclusion. Thank you for your question about wine mixed with gall.