To slice text in Affinity Photo in parallel lines, create some text or use an existing design, select that and then go to the convert to curves button (or right click and select the item from the menu).
You now have curves or a path you can use with the geometry command. Create a thin line using the rectangle tool, set the color to something that easy to identify and different from the previous.
Hold down the alt / opt key and drag and duplicate the lines, multiple times, say 30 times etc. Select them all and go to the alignment tools and align middle
Use the distribute tools (if not available via them via the view menu and customize toolbar) and select the distribute horizontal center so now all the rectangles are equally spaced and equally sized. You can then select them all and drag on top of the converted curves and position on top or to the side etc (if you only want to use the geometry commands with part of the the artwork. Go to the layers and drag all the curves out from the group so they are the same level as the rectangles. Select all the layers.
Go to the layer menu and geometry and divide. You can see the artwork has been broken into lots of fragment. Select all the parts of the original lines (in red, green or whatever color you selected) and delete them and you are now left with your line design.
You don't have to use the artwork at 90 degrees, you can always rotate the art say to 45 degrees to create a diagonal design.