The success ratio of degrafting/rooting of Astrophytum depends upon each species. Myriostigma rooting is easier than asterias.
If grafting stock was Hylocereus the joint is embedded deeply in the scion and there will be a deep cavity after removed joint completely.
This deep cavity may be a cause of rotting during rooting process.
To minimize this problem I cut scion bottom just above the joint.
The photo is grafted myriostigma, cutting off last autumn and put in on a empty back plastic pot.
Roots came out in this spring and I potted.
The following method is commonly used in Japan for some species, difficult rooting.
This method is called "Zuioroshi" meaning degrafting with vascular bandles.
I use this method for quite many asterias and Ariocarpus fissuratus grafted on Hylocereus. A. fissuratus is difficult to stop liquid coming out from cutting face.
Initially roots come out from the vascular bandles and plants rely on the roots but own roots come out later.
Since there was no soft tissue, you can bury the vascular bandles into pottingmix.