That depends on what you mean by "mini tornado," as there is no real definition for the term. Some people apply the term to whirlwinds such as dust devils, which aren't really tornadoes. In that case, then no.
Sometimes, especially outside of the U.S. tornadoes with relatively narrow damage paths are referred to as "mini tornadoes," regardless of intensity. In that case, such a tornado may be able to lift up a cow depending on how intense it is.
One tornado in France in 2008, which some outlets called a "mini tornado" caused isolated F4 damage. Such a tornado could pick up cows and much larger objects.
No, tornadoes do not typically pick up and carry cows through the sky.
No. It might be able to pick up a new-born calf, but not a cow.
Yes. A strong tornado in the range of EF2 to EF5 can pick up a bus or even a train.
Keep on eating up mini tornadoes
The maximum weight an average tornado can pick up is estimated to be around 30,000 pounds (15 tons). However, stronger tornadoes have been known to pick up heavier objects.
"I'll pick you up later."
A dust devil is called a mini tornado because it looks similar to a tornado in appearance, with a spinning column of air picking up dust and debris. However, dust devils are much smaller and weaker than tornadoes, typically only reaching speeds of up to 60 miles per hour.
No. Though a very strong tornado might cause it to collapse.
That is extremely difficult to estimate and would depend on the size and strength of the tornado and what there is to pick up. A large, violent tornado moving through a developed area might be carrying many thousands of small objects.
An EF0 tornado can't pick up much of anything, so probably not.
A cow is born.
No. A skyscraper is far to heavy. However, an EF5 tornado may cause a skyscraper to collapse.