The way to get past speech blocks is by letting yourself stutter. You start working on this my making the sound you're afraid to make and therefore block on. You can only start this work on the easiest and safest of situations. If you try and do it when it's too difficult you won't be able to. You need to baby steps your way up. If you're only either fluent or blocking, that shows you probably have a lot of shame around stuttering and are unwilling to show any of it. You can start on the journey to move past this by trying to make sound, even if it's ugly and weird.