Before cutting shoots, ensure that the plant is dry and will remain so for 2 or 3 days. Water plants in pots 24 hours before cutting.
If the shoots have developed on the stem (trunk) of the aloe, simply cut them with a sharp secateur or knife.
If they start showing from under a stemless or sitting plant, scrape away the soil underneath the shoot(s) to enable you to cut as close to the main plant as you can. I use a carpet knife blade or scalpel for this. Be careful not to slip when the blade cuts through the shoot as you could damage other parts of the plant (or yourself).