check-new-release process eating up resources on Ubuntu server 13.04

Try doing

apt-get remove ubuntu-release-upgrader-core

The script that you're seeing running is /usr/lib/ubuntu-release-upgrader/check-new-release, and removing the above package will remove that script completely.

A description of this package is:

ubuntu-release-upgrader-core - manage release upgrades

In the file /etc/update-manager/release-upgrades change Prompt=normal to Prompt=never.

You can also do this through the GUI, but that may not be appropriate for a virtual server.

You can do a manual check for a new release with do-release-upgrade