What does science say about this technique? Are there any scientific proofs that back your claims?

The Mirror Tapping Technique is based on another popular technique called "EFT" or "Emotional Freedom Technique". In other words, the Mirror Tapping Technique is an enhanced version of the Emotional Freedom Technique and contains all elements and practices of the Emotional Freedom Technique, plus more. 

• Rigorous scientific research, clinical studies, and over 100 papers published in peer-reviewed professional journals show that this technique is an "evidence-based" method.
• Studies show that this technique is effective as a self-help tool, while it is also used in many healthcare settings by medical and mental health professionals.
• This technique has been scientifically proven to be hyper-effective for healing, treating, and overcoming a variety of psychological, emotional, and physical conditions.
  

You can find links to over 100 clinical trials, studies, and research papers here, and you can also Google "EFT research", "EFT study" or "EFT clinical trial".

Example 1: War Veterans Heal & Overcome Severe Post-Traumatic Stress Disorders Quickly & Dramatically - Without Any Drugs or Talk Therapies

Research by the National Institute for Integrative Healthcare showed that 8 out of 10 war veterans with severe PTSD who practiced this New Mind Reprogramming Technique no longer tested positive for PTSD. They got better and stayed better fast. Symptoms disappeared dramatically and quickly after treatment with New Mind Reprogramming Technique.

Example 2: More Effective In Healing Depression Than Drugs & Talk Therapies

A study published in Explore: The Journal of Science and Healing found that this technique has a very large treatment effect on healing depression, and is more effective than drugs or talk therapy (Nelms & Castel, 2016).