You can indeed replace your landing paper (officially known as an IMM 1000 Record of Landing). This process is called verification of status: http://www.immigroup.com/replacement-copy-record-landing-verification-status.
However, you cannot use it to travel. Do you have a PR Card? That is how you can travel from and to Canada. If you do not have a valid PR Card, you will have to replace your record of landing first, and then apply for the PR Card: http://www.immigroup.com/permanent-resident-card