Hi Mark -
Congratulations on making the switch to the Modern UI - I trust that you'll find the speed boosts and newfound flexibility are worth it.
The Modern UI templating system uses Freemarker - a quick overview of Funnelback's usage of Freemarker is available at:
http://docs.funnelback.com/freemarker.html
Equivalent functionality to s:Cut in Freemarker can be seen in the default Modern UI form (simple.ftl) when removing the 'http://' prefix on results' URLs:
...
<@s.cut cut="http://"><@s.boldicize>${s.result.displayUrl}
...
Similar functionality can be achieved using the Freemarker 'replace' built-in directive:
...
<@s.cut cut="http://"><@s.boldicize>${s.result.displayUrl}
...
Happy templating.