How does shahadah demonstrate peace?

Shahadah means testimony , in Islamic perspective it means giving testimony that a person believes in Allah and the Prophet Muhammad ( peace be upon him ) . If a person really and truthfully does give testimony of his belief then he/she is has to adhere to teachings of Islam .

And Islam teaches peace and avoid mischief , war and other things which cause problem to other humanity . Some of the few verse are as below

( Quran , Al-Maeda, Chapter #5, Verse #16) : " Wherewith Allah guideth all who seek His good pleasure to ways of peace and safety, and leadeth them out of darkness, by His will, unto the light,- guideth them to a path that is straight. "

( Quran , Al-Anfal, Chapter #8, Verse #61) : But if the enemy incline towards peace, do thou (also) incline towards peace, and trust in Allah. for He is One that heareth and knoweth (all things). ( Quran , Az-Zukhruf, Chapter #43, Verse #89) : But turn away from them, and say "peace!" But soon shall they know!

( Quran , Al-Hujraat, Chapter #49, Verse #10) : The Believers are but a single Brotherhood: So make peace and reconciliation between your two (contending) brothers; and fear Allah, that ye may receive Mercy.

(Quran , Al-Araf, Chapter #7, Verse #56) : Do no mischief on the earth, after it hath been set in order, but call on Him with fear and longing (in your hearts): for the Mercy of Allah is (always) near to those who do good.

these are only few verse .. there are many verse which praeach to keep peace and not to do wrong and mischief .

Hope that answers your question . Allah knows better .