In general, a wet saw is the best for cutting travertine tiles. But, a tile cutter, an angle grinder with a tile attachment, and a dremel with a tile attachment will also work. However, they take far longer to make cuts than a wet saw. Especially, for thicker travertine tiles.
As a general rule, tin snips or a hacksaw can be used. As well as, the following tools provided a metal cutting blade is used: scroll saw, oscillating multi-tool, metal lathe. Other options are a plasma cutter, laser cutter, CNC machine, and a table saw.