WalterBeiter

It's a little convoluted at the moment, just because you can't just click a path and press ⌫, and the Break Curve command doesn't yet work on multiple points at once.  Anyway, here are the steps.
 
1: Make sure your shape is made of curves (which yours already is, but for ellipses, rectangles, cogs, etc., press ⌘⏎ to convert the shape to curves.)
2: Using the Node Tool, click on one of the nodes adjacent to where you want the break.
3: Click the Break Curve button (the first button in the Action group of the main toolbar.
4: Still using the Node Tool, click the other node.
5: Click the Break Curve button.
6: Deselect.
7: In the Layers panel, find the newly created shape (the segment you cut out), then delete it.
 
Hope that helps!
—Russ

If you want to hide the UI temporarily, just hold Space and the tool UI will disappear :)
 
Ultimately, corners will be a property on the shapes so they won't force the shapes to become curves - I think that'll be a nice addition :)
 
 
-> very good news.. Thanks a lot. Looking forward to new updates.

Hi WalterBeiter,
 
Glad you like the corner tool! :)  It's a bit slower at the moment than it will ultimately be - I have two methods for working out the equations that I need and one of them is slow but reliable, while the other is super-fast but very occasionally goes a bit wonky... so we're using the slow one at the moment until I get chance to debug and fix the other one! So one day it'll get a LOT faster! It shouldn't be a problem once you've created the corners though as they don't require extra processing until you adjust them again - so hopefully this doesn't interfere with your real-world drawing (although I can definitely see how it can be provoked in test-cases)
 
If you want to hide the UI temporarily, just hold Space and the tool UI will disappear :)
 
Ultimately, corners will be a property on the shapes so they won't force the shapes to become curves - I think that'll be a nice addition :)
 
Thanks again,
Matt

Hello WalterBeiter,
 
- change the document size by removing 4mm from the width field in the Document Setup dialog;
- make sure that Anchor to Page is enabled, and set the Anchor to the middle of the square. Click OK.
 
This should remove 2mm from each side without affecting object's positions in relation to the page.

plug-ins would indeed be great. There is a lot of potential. 

Wow, great tool!
And the Astute Graphics guys have a great set of plugins.
Is it possible to add the Illustrator plugins support in Affinity?

When selecting a Push Tool the cursor changes to circle. Then, when you start pushing the object it changes the object's shape. It does not cut, add, merge, divide or else, just deforms the shape.
It would be nice, also, to choose the cursor shape between circle or square or even something else for interesting effects.

Please let me easily transform any vector object. With a transform tool I could set the perspective right, and distort groups and other objects. 
For instance: I have a group of rectangles, and I want to transform and distort this group as if it was a line. 
I have a rectangle and I want to put it in perspective, or make a 3D effect. It would be great either have a transform tool similar to photoshop and the ability to select for instance the outer corners of a rectangle and option drag them towards the middle in the same amount. 
 
I definitely need a line tool. I want to edit every single bit of a line. I the ability to make a dashed or a dotted line. Of course I could use cmd-j, but I want it as a line so I can distort it. Also I want dashed lines for rectangles, etc. It would be great to turn a group of objects into a line, like when you have a couple of objects and you want to put them on a path and behave like they were a line.