You should not use a hand mixer to cut butter into flour although you technically could if you're very careful, but it's not recommended.
Instead to cut cold butter into the flour or other dry ingredients without a food processor it's best to use a pastry blender or your fingertips for cutting the butter into the flour.
Using a hand mixer to cut butter into flour is not recommended because the beaters will warm and melt the butter quickly, instead of creating the small and distinct, pea sized pockets of cold butter that are needed for producing the flaky, airy texture in pastries, pies as well as biscuits.
Instead of using a hand mixer for cutting butter into flour you can instead use a pastry cutter or blender, box grater or even just your fingertips.
To use your fingertips to cut the butter into the flour, simply toss the butter in the flour and then coat the butter.
Next quickly flatten the pieces of butter between your thumb and your fingertips until you form flaky and pea sized clumps of butter.
For the box grater, freeze a stick of butter for 15 to 20 minutes.
Then grate the frozen stick of butter directly into the flour to get perfectly uniform and cold pieces of butter.
For the pastry cutter or blender, press the metal blades straight down into the bowl with a rocking motion until the butter has reached the desired size.
Most biscuit and pie dough recipes call for cutting butter into flour, which simply means to work cold butter into dry ingredients until pea-sized pieces are evenly mixed in.
This method results in super flaky, tender pastries.