To me, the only way you can do that is via a block rewrite by creating a module so in app/code/local/Vendor/Module/Block/Page/Html/Breadcrumbs.php
:
<?php
class Vendor_Module_Block_Page_Html_Breadcrumbs extends Mage_Page_Block_Html_Breadcrumbs {
public function removeCrumb($crumbName)
{
if (isset($this->_crumbs[$crumbName])) {
unset($this->_crumbs[$crumbName]);
}
}
}
Then in app/code/local/Vendor/Module/etc/config.xml
:
<?xml version="1.0"?>
<config>
<modules>
<Vendor_Module>
<version>0.0.1</version>
</Vendor_Module>
</modules>
<global>
<blocks>
<page>
<rewrite>
<!-- Mage_Page_Block_Html_Breadcrumbs -->
<html_breadcrumbs>Vendor_Module_Block_Page_Html_Breadcrumbs</html_breadcrumbs>
</rewrite>
</page>
</blocks>
</global>
</config>
And finally app/etc/modules/Vendor_Module.xml
:
<?xml version="1.0"?>
<config>
<modules>
<Vendor_Module>
<active>true</active>
<codePool>local</codePool>
<depends>
<Mage_Page />
</depends>
</Vendor_Module>
</modules>
</config>
Then you should be able to do the following in your layout XML file:
<reference name="breadcrumbs">
<action method="removeCrumb">
<crumbName>Home</crumbName>
</action>
</reference>
Replace Home
with whatever crumb name you need to remove.
NB: actually I'm pretty sure it could be possible to do it via an event observer on controller_action_layout_generate_xml_before
I'm just not 100% sure how to tacle this one.