Sarah Palin has no love for the daddy of her grandson ... because she just barked out to TMZ that Levi Johnston is a 'deadbeat dad.'

As TMZ previously reported, Levi just filed legal docs asking for 50/50 joint custody of 4-year-old Tripp.  He says it's in the boy's best interest.

As for whether Levi should get joint custody ... Palin is incredulous.

But here's the rub ... Levi is roughly $66k behind in child support.

Palin's disdain for Levi is palpable.  Watch the video ... you'll see.