Unfortunately, XSLT is not supported in Gloop. However, in Gloop, if a field is empty and you don't want it in the JSON or XML at all, set the required property of that field to false, set allowNull to true in the Properties View of that property, which are already the default, then, if it's null it won't be written out during the serialization.
Support for XSLT in Gloop
Support for XSLT in Gloop
Can I use XSLT files to handle blank fields in my XML so it will not be included when my Gloop service receives the XML from the request?