Na should be "not."

Wee, sleekit, cowrin, tim’rous beastie, O, what a panic’s in thy breastie! Thou need na start awa sae hasty,

"Translation"/update to more standard current English:

Small, sleek, cowering timorous beast

Oh, what a panic in your chest.

You need not start away so quickly.

Googling for short foreign words that look like misspelled English words is gonna be tough. I recommend something like the Online Scots Dictionary: https://www.scots-online.org/dictionary/scots_english.php

I am not competent to rate the linguistic quality of this translation, but it certainly is amusing: https://www.youtube.com/watch?v=gQXpznIhT08 .

awa = away, sae = so

He’s saying the mouse needn’t leave so quickly.