How remove description and slug fields from taxonomy

Adding a new field to the new term form is pretty simple, hook ‘add_tag_form_fields’ and echo out the field if the passed taxonomy slug matches yours.

Removing and adding columns is more involved, but doable. Most of the scarce documentation involves columns in the posts list table, but the same principles apply to terms list tables. These are the best references I know of:
Custom Columns for Custom Post Types

Modifying Administration Tables

The only way to remove the existing form fields in PHP would be to rewrite the entire admin screen, remove the original from the menu and add your modified version. Resolving all possible links to your new admin screen could be difficult.

A better approach will likely be to use javascript or jQuery to hide the fields with CSS once the page loads.