The sample image is very small and has jpeg compression artifacts, so it is hard to work with.
What sort of cutter are you using? A reel based vinyl cutter that feeds in the printed substrate... Or a flatbed CNC cutting table?
What tolerance does it have for cutting accuracy? +/- 0.5 mm etc?
I presume that your cutting paths are vector? How are they generated?
I would likely favour using a vector contour edit to shrink the cutting paths inwards slightly so that you are aiming for original or "real" pixels.
Then whatever method you use to create bleed the cutter will be targeting "proper" content and not the "invented" bleed content.
Two approaches come to mind:
1) Work on a duplicate layer. Selecting the white area, but better if you already have a transparent background. It might be best to expand this selection so that it goes into the image area slightly rather than the in-between antialiased edges. Use content-aware fill. Inverse the selection so that only the objects are selected and not the trim areas. Expand the selection a little bit more. Add a layer mask. You should then have the original "clean" elements on one layer and the bleed on another below.
2) Another method... Remove the white background so that you have transparency. Duplicate the layer and then run Filter > Other > Minimum to expand the pixels and then to layer this under the original layer so that is covered by the original, except for the edges that have been expanded.
These are just general suggestions, there may be more steps required, such as making better masks, or using edge masks, or retouching where the bleed touches the original pixels etc.
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