Thought today I would show and explain how I rip when I have made a mistake in my paper piecing. The example really happened to me today so decided to take step by step photos as I was doing it. The mistake I make the most is stitching a wrong side of a fabric to a right side of a fabric. You don't have to toss the block and start over just because it is on paper but you can take the offending fabric off and preserve the paper without it tearing.
Step one - lay the paper side down on the table and lift the top fabric so you can see the stitches between the two fabrics.
Step two - start clipping those threads very carefully with a sharp pointed pair of scissors all the while pulling gently back on the top fabric to reveal more stitches as you clip.
Step three - You need to remove the thread that is still in the two fabrics and picking it out by hand takes a long time. What I do is use a piece of Masking Tape or Painter's Tape and lay it on the threads, press it down only on the threads then remove it. The threads will stick to the masking tape not to the fabric and pull right out. Do the same thing on the paper side of the block to remove any small threads too.
This example shows the threads removed and no torn paper only holes where the needle pierced the paper when it was stitched that first time.
Step four - Place your fabric back in the correct position and insert in the machine. To start stitching you need to line up your needle exactly in one hole that was made the time before. Most machines will take exactly the same size stitches so this row of stitching should follow the same holes from start to finish and not rip the paper.
This example shows what the re-stitched seam looks like - no ripped paper.
Now wasn't that cool! When I discovered this way of ripping it has made paper piecing much more enjoyable. This section of the block I was working on today only had two pieces of fabric but some blocks have many pieces and starting over on those kind of blocks is not fun.