Restriction enzymes, or restriction endonucleases, or base pair cutters, cut doubled-stranded DNA by disrupting the phosphodiester bond that joins adjacent nucleotides. It is not random though.

Like other enzymes, restriction enzymes show specificity for certain substrates. For these enzymes, the substrate is a sequence of base pairs in the DNA strands. They bind to, recognize, and cut (digest) DNA within specific sequences, called restriction sites, and these sites must be palindromic readings from the separate strands. You can have 4, 6, or 8 (there are others) base pair cutters. If the sequence is shorter (say a 4 base pair cutter), it is more likely to be repeated than an 8-base pair cutter.

The biochemistry behind it is ridiculous and goes into why enzymes cut at the free ends of DNA molecules, while restriction enzymes cut inside the DNA strands.