How can I skip trigger execution?

You can implement that logic by yourself. You can write an UtilClass to check if you execute or not the skip Trigger Logic

public class ByPassUtils { public static Map triggerNameBypassed = new Map(); public static void ByPass(String triggerName){ triggerNameBypassed.put(triggerName,true); } public static void UndoByPass(String triggerName){ triggerNameBypassed.put(triggerName,false); } public static Boolean isByPassed(String triggerName){ return triggerNameBypassed.hasKey(triggerName) && triggerNameBypassed.get(triggerName); } }
logic when you want to bypass (maybe in the case trigger for your example)
ByPassUtils.ByPass('TaskAfterUpdate');
in your trigger code (in your case TaskAfterUpdate)
if(!ByPassUtils.isByPassed('TaskAfterUpdate')){ // your logic here }