Depending on how your skin is constructed, you can insert a style on that page to disable display of the breadcrumb.
For example, on a site that I have, if I set this style:
.skinheader{display:none;}
The result is that the entire section with the skinheader style is suppressed. That gets the breadcrumb text, the braile-like symbols that surround it, the horizontal bar, and also the current date.
If, instead I set:
#dnn_dnnBREADCRUMB_lblBreadCrumb{display:none}
then only the breadcrumb text is suppressed.
That particular skin isn't set up to suppress display of the entire breadcrumb and only the breadcrumb. In your case, you could edit the skin such that a single class or ID controls the part that you want to suppress, and then you can do that by applying a style for that class or ID on only that page. You can do that by putting the style somewhere in the header or footer of a module that is only on that particular page.
This tutorial:
Troubleshooting DotNetNuke Skinswill show some techniques to help identify classes and IDs on a page. Also, the Web Developer's Toolbar is a great way to interactively test CSS.