She's not the one who cut the rope.

After the events of the rope cutting her boyfriend Damien just disappears and she doesn't understand why.

She was so upset and found out she was pregnant and since she was hurting (and Bree, O's sister in law, encouraged it) decided it was best to abort.

It comes out later that Damien left because him and Bree were sleeping with each other (they slept together 4 times) and I guess him and Bree felt it was best he leave.

After finding out him cheating Olivia eventually gives Damien a cd that shows their baby and he cries about it.

Olivia ends up confronting Bree.