"mul" can stand for "minulla" in spoken Finnish. The sentence decides its meaning.
Spoken form of 'minulla': the last syllable drops
mul, mulla
These are related spoken alternatives. Which one you hear varies by speaker and situation. Check each example rather than treating them as interchangeable in every sentence.
Ei kiitos, mul on oma kassi. - No thanks, I have my own bag.
mul here: I have (lit. 'at me') - spoken 'minulla'
Written Finnish: Ei kiitos, minulla on oma kassi.
Mul on kaks veljee. - I have two brothers.
mul here: I have - spoken 'minulla'
Written Finnish: Minulla on kaksi veljeä.
Mul on kuumetta. - I have a fever.
mul here: I have - spoken 'minulla'
Written Finnish: Minulla on kuumetta.
Sopiiks, et mul on kissa? - Is it okay that I have a cat?
mul here: I have - spoken 'minulla'
Written Finnish: Sopiiko, että minulla on kissa?
No ku mul oli niin kiire. - Well, 'cause I was so busy.
mul here: I had - spoken 'minulla'
Written Finnish: No kun minulla oli niin kiire.
Mul tuli just mieleen yks juttu. - I just remembered a thing.
mul here: to me - spoken 'minulla'
Written Finnish: Minulla tuli juuri mieleen yksi juttu.
Spoken and written Finnish are different registers. The examples show how "mul" is used here and pair it with the written sentence. Learn the meaning in context rather than replacing every occurrence of a word.