Diplomacy - dislodged unit still disrupts another?
Each unit has one potential action each phase. But each year has five phases:

Spring movement
Spring disband/retreat (if needed)
Fall movement
Fall disband/retreat (if needed)
Build/break (if needed)

Dislodged units (normally) still cut support. Because they cut support in the movement phase and are dislodged in the retreat/disband phase. There are a few exceptions where support is not cut, but that is not for this setting.
In this case, we have 6 units with their orders:

Let's first check the support orders:

Turkey: A lvn Supports  A mos -&gt; stp. This support is cut because of (A pru -&gt; lvn).
Germany: A sil Supports  A war -&gt; pru This suport succeeds.

Next the moves.

Turkey: A mos -&gt; stp (unsupported so strength 1, fails because A stp holds with strength 1).
England: A stp Holds (succeeds)
England: A pru -&gt; lvn (move fails, but still cuts support)
Germany: A war -&gt; pru (supported strength 2 so the move succeeds).

The failed orders are shown below:

Now it is time for retreats/disbands

England: A pru is dislodged and can only move to Berlin.

This is the relevant quote from the rules:

A  unit  being  dislodged  by  one  province  can  still  cut  support in another province. Just as a unit being dislodged by one province can still cause a standoff in another, a unit still manages to cut support even if it’s dislodged. Just make sure  that  the  dislodgment  isn’t  coming  from  the  province  where  the  unit  is  giving  support.  (Remember  this  rule:  A  dislodged  unit,  even  with  support,  has  no  effect  on  the  province that dislodged it.)