The gospel account in Luke chapter 20 from verse 27 to the end gives Jesus' exact words to the Sadducees. This is the text that needs to be looked at hermeneutically, and not the Exodus 3:6 one, which will become clear when the particular verse is copied below:
"Now, that the dead are raised, even Moses shewed at the bush, when he
calleth the Lord the God of Abraham, and the God of Isaac, and the God
of Jacob. For he is not a God of the dead, but of the living: for all
live unto him." Luke 20:37-38 K.J.V.
Jesus quoted from Exodus 3:6, showing God to be the originator of those words. (See Exodus 6:3). Jesus confirmed the truth of Moses' words, quoting him, and agreeing, plus adding a bit more: that they live unto God. This shows why the Sadducees were silenced.
Note that the account does not say the Sadducees were convinced by Jesus' argument! They were left without a leg to stand on, and Jesus' rebuttal of their wrong theology contributed to the Scribes and the Pharisees giving up on trying to trap Jesus with questions that would enable them to hand him over to the Roman authorities (Luke 20:20).
Note also, that the Scribes agreed with Jesus' argument, for the Scribes believed in the resurrection of the dead. The Sadducees did not (hence their trick question on marriage in the resurrection). Jesus' proof from the lips of Moses delighted them, for (on that point) they agreed with Jesus. But the Sadducees never said Jesus had convinced them. They just had to zip it, and stop trying to trip him up with their malintentioned questions.
As for what Moses said, it was a point further to the way God had identified himself to him as having the name, "I AM". Moses quoted God as saying to him at the bush,
"Thou shalt say unto the children of Israel, The Lord God of your
fathers, the God of Abraham, the God of Isaac, and the God of Jacob,
hath sent me unto you; this is my name for ever..." Exodus 3:14-16
K.J.V.
Given the length of time those three forefathers of the nation of Israel had lived, and how bone-dead all of them were by then, God was saying he was still their God. Impossible, unless those three were alive in another way. Then, when Jesus agreed, quoting all of that, he showed that Abraham, Isaac, and Jacob remained alive thousands of years on, with God still being their God. And, to top it all, Jesus took the name of "I AM" to himself (John 8:58). No wonder those who hated Jesus (including the Scribes), wanting to silence him and having failed to do so with their words, resorted to trying to stone him to death, and when that failed, got him handed over to the Roman authorities.
The grammatical choice of words in Exodus 3 and Luke 20 is deliberate in both instances. The present tense teaches massively important truths as to the name of God and how that bears on God still being the God of those who died in faith, but who have passed over from death to life.