I was told Jesus is without sin. But on Easter, at Mass I heard a reading that said, “Jesus died to sin.” Which is true?

You are quoting Romans 6:10 which says, "the death he died, he died to sin, once for all.” In saying that Christ “died to sin,” St. Paul is not saying he died on account of his own personal sins. The Greek word hamartia (Sin), Is often used by St. Paul to refer to our own personal sins. But it is also used to refer in a more collective sense to the sin of the world. For, this fallen world of ours, is immersed in sin, in an attitude of rebellion pride, greed, lust, and so forth. And this climate of sin, is like a force, a mindset, initiated by Satan, and connived in by human beings. It is to this world of sin that Christ died. He broke its back, by dying to it, and rising victorious over it. And he defeated it in the most paradoxical way: he conquered pride, by humility, disobedience by obedience, and death, by dying and rising. 
 
It is to this regime of sin, that Christ died, not his own personal sins of which scripture is clear, he had none. (cf 1 Peter 2: 22) 
 
In the same chapter (6:2, 11), we are taught to realize that we too have died to sin, and that this world of sin is to have no more power over us. We must come to experience increasing power, authority, and victory over the influence of this world of sin. We are to lay hold of the life which Christ offers us wherein this world of sin has no more power over us.