Cutting is a sharp transition into the next record. They are fairly easy to do. Once the two records are beatmatched all you have to do is quickly fade over to the other record. What takes practice is timing the cut so it transitions right where you want it to.

When you are cutting you want to make the transition right in between the two beats. It is also preferable if you cut right at the end of a bar on one record and into the beginning of the bar or the other record.

One way you can cut into a song exactly where you want to is by doing a drop-mix cut. To do this, you cue up the second record to the part you want to cut into. When the timing is right, start the record at that point while at the same time cutting into it.