I blend twice. I blend for a few minutes, then put the peppers in a pan with vinegar and salt and once soft they go back into the blender with the rest of the ingredients until it's smooth.

I blend my sauces in a blender and add a very small amount of xanthan gum to stabilize it and bring it up to the thickness that I want.

Usually I strain it. The tool I use is called 'flotte lotte' in German. And then I take the strained rest and press it through a nut milk sack and press every little precious drop of juice out. The residue of that process is quite dry already. Sometimes I dry this further in the oven and grind into a powder as a spice. But the drying process leaves the kitchen in a firey hot breeze. My wife hates it when I do this.

You can try using a sieve or food strainer. Put your mash on the strainer and push it through with a wooden spoon. I recently purchased a food mill and love it. It really does the trick. I use it for tomatoes when I'm making tomato sauce too.