There are always a need to disable my Site and My Links in MOSS 2007. Below are the steps inorder to disable the links -
1> Go to the Sharepoint Central admin page.
2> Then go to the SSP admin page.
3> Under the User Profiles and My Sites, click on the link "My Site settings".
4> In the left pane, there is a link "Personalization Services Permission". Click on that.
5> Select the user "NT AUTHORITY\authenticated users" and click on modify permissions of selected users.
6> Uncheck "Create Personal Site" and "Use Personal Features" and select "Manage Permissions" or any other permissions.
This shall fix the issue of removing the My Site and My Links from a Sharepoint Site.