You're confusing things.
- "Allah subhanahu wa ta'ala" (meaning "the most glorified, the most high")
- "assalamu alaikum wa rahmatullah" (meaning "peace and mercy of Allah be upon you")
The first one is meant to praise Allah, and in doing so we mean he is exempt from evil doings. Of the dictionary meanings of تسبیح/سبح/سبّح is: عَظَّمَهُ وَمَجَّدَهُ وَنَزَّهَهُ ( glorify, magnify and know him free of any wrong/evil/misconduct)
Many times in Quran you will see the phrase سبحانه or سبحانک as in you're exalted. Perhaps among the most heard verses is:
They said, "Exalted are You;
لَا عِلْمَ لَنَا إِلَّا مَا عَلَّمْتَنَا ۖ إِنَّكَ أَنتَ الْعَلِيمُ الْحَكِيمُ
we have no knowledge except what You have taught us. Indeed, it is You who is the Knowing, the Wise."Baqara 32
It's like the angels saying, oh no no no no, sure sure sure we know you are free from any error/evil doings.
Has your life ever gone so south that made you say or hear " Oh God, when will my misery end? ", "God why did you do this to me?" "God you killed those innocent children!!!" , " God why can't I also be rich?", "Why did you send an earthquake and kill all those families?"
But Allah is free from ALL wrongdoings.
The second one is meant as a form of dua. May Allah bring his bless you with his bounty and mercy.
So in the first phrase the focus is on Allah.
In the second phrase the focus is on bringing (making dua) for the blessing and mercies of Allah onto that person.