In order to reach the goal of this question, we must propose different ways. In fact, we can not only propose a solution. By combining different techniques you can achieve the desired goal. You can reduce a vector file size in Illustrator through following tips:
Extend all live effects: brushes, patterns, symbols, type etc. You should crop some brushes and Patterns, so that remove transparencies/unfilled paths.
You should reduce blending to minimum steps to reduce a vector file size in Illustrator (25–30 steps, you should not Smooth color, this is usually useless job), simulate drop shadows by using blends; also you should remove all tools from Illustrator palettes (brushes, swatches, styles and symbols).
You should check the below route
Window —> Document Info —> Linked images
You find at the address if there are link and embedded images. You should clear all of that.
You should see (Window —> Flattener Preview) and check Regions that you might rasterize it. You should work on regions that are raster to reach the complete vector output. When you use gradient your file may become raster (it occurs when using radial gradients) on top of each other. Drop shadows and blurs and gradient can make vector file heavy. So you should avoid them to reduce a vector file size in Illustrator.
Is it possible to save as another format to reduce a vector file in Illustrator?
Of course there is a way to reduce your vector file size by saving it with another format. Follow the route to save your file as PDF:
File —> Save as
Choose Adobe PDF (*.PDF) in ‘save as type’ box and click save.