I heard some people pronounce it as doesn' and I am curious if this pronunciation is common and okay to use in day-to-day conversions.
As a Brit who really only knows American English from TV, I'd have thought they would more commonly elide to don't, in a similar fashion as ain't from isn't [even though it could be argued they are dialectical].
Equally, in the UK, doesn't will often be elided to dunt [or in some accents to don't]. Isn't would be elided to int, in the same vein. [I've never seen these written, only spoken.]
Isn't it has a special case of being elided further, to innit.
There seems to be a commonality of dropping the s rather than the t, which may still remain as a glottal stop.
This is due to "elision":
the omission of a sound or syllable when speaking (as in I'm, let's) Lexico
But "doesn't" is always more commonly used.
You can use doesn' in day to day conversations, but it's better to stick with doesn't.
Speech as in the example is not a general feature in American English.
"American accent", however, is not a single accent, but many. For example, among speakers of African-American Vernacular English, a range of dialects common for many Black Americans, may occur speech as in the example.
The effect may be described from the following passage in the article from Wikipedia:
Final consonants may be deleted (although there is a great deal of variation between speakers in this regard). Most often, /t/ and /d/ are deleted. As with other dialects of English, final /t/ and /k/ may reduce to a glottal stop. Nasal consonants may be lost while nasalization of the vowel is retained (e.g., find may be pronounced [fãː]). More rarely, /s/ and /z/ may also be deleted.
As suggested, AAVE is not a prescription followed by everyone within a group. The specific effect is simply one observed among certain individuals. As noted also, the same effect may appear in other dialects outside of AAVE.