Some say Jesus was already dead by the time the soldier pierced Jesus’s side, and others say the soldier’s spear killed him.  Let’s take a closer look at the two views.

First View: Jesus died before the solder pierced His side with a spear

This view is supported by the account in John.

Joh 19:30  So when Jesus had received the sour wine, He said, “It is finished!” And bowing His head, He gave up His spirit.
Joh 19:31  Therefore, because it was the Preparation Day, that the bodies should not remain on the cross on the Sabbath (for that Sabbath was a high day), the Jews asked Pilate that their legs might be broken, and that they might be taken away.
Joh 19:32  Then the soldiers came and broke the legs of the first and of the other who was crucified with Him.
Joh 19:33  But when they came to Jesus and saw that He was already dead, they did not break His legs.
Joh 19:34  But one of the soldiers pierced His side with a spear, and immediately blood and water came out.

Jesus said, “It is finished”, and then died.  The soldiers later came and saw that Jesus was already dead.  Rather than breaking His legs one of the soldiers pierced His side with a spear.

Second View: Jesus died by the soldier piercing His side with a spear

This view looks at the account in Matthew.

Mat 27:49  The rest said, “Let Him alone; let us see if Elijah will come to save Him.”
Mat 27:50  And Jesus cried out again with a loud voice, and yielded up His spirit.

This view claims that verse 49 is missing some additional text at the end of the verse.

And another took a spear, and thrust it into His side, and out came water and blood.

There are a few (about 7) manuscripts which have this additional text, but the vast majority do not.  If correct, then Jesus died by being pierced by a spear.  Furthermore, John 19:34 then has to be translated as:

Joh 19:34  But one of the soldiers had pierced His side with a spear, and immediately blood and water had come out.

In the Greek, “pierced” is in the Aorist tense and “came out” is in the second Aorist tense.  These tenses allow for the English “had” if it makes contextual sense.  So this view is feasible.

Which View is Correct?

The second view suffers from some weaknesses.

Firstly, it relies on just a few manuscripts.

Secondly, perhaps the meaning of the addition text is that it happened later rather than at that moment.  So,

And later another took a spear, and thrust it into His side, and out came water and blood.

rather than,

And at that moment another took a spear, and thrust it into His side, and out came water and blood.

If the meaning is that it happened later then the additional text actually supports the first view.

Thirdly, it makes the order of events odd to say the least.  At some point before Jesus died, a soldier must have walked past Jesus hanging on the cross and decided to thrust his spear into Jesus but leave alone the two criminals hanging either side of Him.  Then sometime later the soldier walked past again but this time broke the legs of the two criminals.  This just seems very odd behaviour and raises more questions.  John 19:31 states that the Jews had asked Pilate if those crucified could be killed by having their legs broken. Why did the soldier kill Jesus sometime before the others who were crucified and why the different treatment for Jesus, that is, why pierce His side but break the legs of the others?

Conclusion

Which view is correct?  Perhaps we cannot know for sure, and perhaps it doesn’t really matter, but for the reasons listed above, it does seem more likely that Jesus died before the soldier pierced His side with a spear.