I have never made beetroot chutney, but I do make jellied beetroot.
If you'd like to give it a go here's how I make it.
Cook peel and dice your beetroot
Put into sterilised jars
Put a raspberry, black cherry or blackcurrant jelly in a jug and make up with half pint hot water and quarter pint malt vinegar and quarter pint cold water.
Pour jelly over the beetroot and shake a little, top up if necessary.
Put a lid on and store in the fridge.
It doesn't last long in our house. We eat it with cold meats and salad.
I've never tried it in a sandwich, it might be a bit wobbly.