How Your Brain Processes Speech
Your brain has to plan ahead when you speak. When you try to say a tongue twister, your brain must send instructions to your mouth muscles about which sounds to make and in what order. With tongue twisters, these instructions come so fast and involve such similar sounds that your brain sometimes sends the wrong signals. This causes you to slip up or say the sounds in the wrong order.
Similar Sounds Create Confusion
Tongue twisters typically repeat similar consonant sounds like 's,' 'sh,' 'th,' or 'p' over and over. Your mouth has to position itself slightly differently for each sound, even though they are very similar. When you try to do this repeatedly at normal or fast speed, your mouth muscles get confused about where to go, and you end up mispronouncing words or stuttering.
The Speed Factor
The faster you try to say a tongue twister, the harder it becomes. This is because your brain and mouth need time to coordinate. When you rush, your brain cannot send clear enough instructions to your mouth muscles, and errors increase. This is why tongue twisters are usually easier to say slowly and become progressively harder as you speed up.
Muscle Memory and Coordination
Speaking involves precise muscle movements in your tongue, lips, and jaw. These muscles are used to certain patterns of movement based on the words you speak regularly. Tongue twisters force your muscles into unusual patterns very quickly. Your muscles have not practiced these exact sequences, so they do not move smoothly, causing stumbles and errors.
Why Practice Helps
The more you repeat a tongue twister, the easier it becomes because your brain and mouth muscles learn the pattern. With practice, your mouth anticipates the movements needed, and the brain's instructions become clearer. This is why tongue twisters are often used to improve pronunciation and speech clarity in language learning and speech therapy. 
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