It's the Library previews that take up a lot of space, not the catalog. (which has the extension LRCAT)
My catalog file is 933 MB, while the previews folder (whose name ends with Previews.lrdata) is 33 GB.
You can move the folder containing the catalog to an external drive, and then double-click the catalog file to launch Lightroom. Note that this may lead to reduced performance. The catalog should ideally be on your fastest disk.
You can keep your photos on the external disk, this will not affect performance.