Rather than removing the unwanted tiddler elements, you can *hide* them using CSS. To learn the class names of the elements, you can display the tiddler in question and then right-click on the elements in question and select "Inspect" (note: the exact menu item text can be somewhat different depending upon your browser).
For your stated use-case, the elements are ".tc-subtitle" and ".tc-tags-wrapper".
Then, assuming the tiddler has a title of "TiddlyWiki CV", you can create a tiddler, e.g. "MyCustomStyles", tagged with $:/tags/Stylesheet, containing
[data-tiddler-title="TiddlyWiki CV"] .tc-subtitle,
[data-tiddler-title="TiddlyWiki CV"] .tc-tags-wrapper
{ display:none; }
That's it.
enjoy,
-e