Affinity Photo lets you erase areas of a layer using a combination of the Erase Brush Tool, the Brushes Studio and the tool's context toolbar. Alternatively, you can use Background Erase to remove pixels from a layer.
You can use the Erase Brush to erase unwanted pixels directly on the layer using the same principles as the Paint Brush Tool.
Background Erase takes a sample of the colour under the cursor when you begin to erase, and will remove all closely matching colours directly under the brush stroke.
As pixels don't exist on a vector layer, a pixel mask is created and applied over the vector layer instead; both vector and pixel layers can be edited using the respective vector tools and layer masking.
in the Layers Studio, you'll notice a white triangular tab appear in the top right corner of the layer entry. Tap this tab to reveal the mask for the layer.