The SVG that gives you only the option to engrave means you very likely have a raster graphic wrapped up in an SVG with no vector data.
Only vectors will cut. The SVG file type can hold vectors and rasters, so if you used a jpg or PNG (raster) clipart image, and just saved it as an SVG without converting it first, you don’t have a vector.
I don’t know your experience level with all of this, so I would suggest looking through the matrix of design tutorials here: Community Glowforge Tutorials: Table of Contents
If you zip and upload the svg here, someone will probably take a look and give a better diagnosis.