Reroute existing wires with autorouter eagle
If you want to do a partial rip up, you need to manually rep up the traces. I believe you can type ripup net (where net is the name of the net you want to remove).

You can select a group of traces with the group tool and then select the rip up tool, right click on the group and select Group: Rip Up.... This will remove only the selected traces. So if you move an IC, you can group all the traces around that IC and rip them up.

If you need to rip up all of the traces and start over, you can do ripup ; to remove all traces from all nets.