In “She said she wanted X”, “she said” and “she wanted” are two different clauses — note that they each have an subject, repeated even though it is the same person. We can optionally use “that” to introduce the subordinate clause.
In “she wanted to get a new car”, there is only one clause, which includes the infinitive phrase “to get X”. This infinitive phrase is not a clause and does not have a conjugated verb. You already know this, so keep it in mind as we look at your other sentence:
In “I saw Tom get into his car and drive away”, there is only one clause (“I saw Tom X”). “Get into his car” and “drive away” are bare-infinitive phrases that complete the meaning of the one and only clause. The work the same as the infinitive phrase in your other sentence (which you understood already).