Young's Literal Translation, Exodus 32:
why do the Egyptians speak, saying, For evil [H7451] He brought them out to slay them among mountains, and to consume them from off the face of the ground? turn back from the heat of Thine anger, and repent of the evil [H7451] against Thy people.
Strong's Hebrew: 7451. רָע (ra') — 667 Occurrences
This word has a wide range of meanings and usages, Strong's Exhaustive Concordance:
adversity, affliction, bad, calamity, displeasure, distress
From ra'a'; bad or (as noun) evil (natural or moral) -- adversity, affliction, bad, calamity, + displease(-ure), distress, evil((- favouredness), man, thing), + exceedingly, X great, grief(-vous), harm, heavy, hurt(-ful), ill (favoured), + mark, mischief(-vous), misery, naught(-ty), noisome, + not please, sad(-ly), sore, sorrow, trouble, vex, wicked(-ly, -ness, one), worse(-st), wretchedness, wrong. (Incl. Feminine raaah; as adjective or noun.).
It could mean as trivial as mischief to as serious as evil.
NIV often provides a modern balanced translation of verses,
Why should the Egyptians say, ‘It was with evil intent that he brought them out, to kill them in the mountains and to wipe them off the face of the earth’? Turn from your fierce anger; relent and do not bring disaster on your people.
In this case, NIV opted to translate the same Hebrew words into two different English words to suit the respective immediate contexts.
The word "evil" is used for what the Egyptians say and the word "disaster" is used for what God does to the people.
Exodus 32:14 King James Bible,
And the LORD repented of the evil which he thought to do unto his people.
New King James Version
So the LORD relented from the harm which He said He would do to His people.
Even the King James translators modernized their old King James' "evil" to the new King James' "harm".
In what sense is the word evil used in Exodus 32:12–14?
Most versions agree that the Hebrew word means harm or disaster when it is applied to God.