How Can I Manually Mock Svg's in my Tests?

Thanks to Jest's transformenter link description here config setting you may do that.

package.json

"jest": {
  "transform": {
    "\\.svg$": "<rootDir>/fileTransformer.js"
  }
  ...
}

IMPORTANT

You need to explicitly provide transform to other extensions (especially *.js and *.jsx) otherwise you will get errors. So it should be something like:

"transform": {
  "^.+\\.js$": "babel-jest",
  "\\.svg$": "<rootDir>/fileTransformer.js"
   ...
}

As for fileTransformer.js it just emulates exporting file's path(you may add any transformation to strip the path or extension or whatever):

const path = require('path');

module.exports = {
  process(src, filename) {
    return `module.exports = ${JSON.stringify(path.basename(filename))};`;
  }
};

It means

import svgIcon from './moon.svg';

will work just like

const svgIcon = 'moon.svg'

So for component containing

...
  <img src={svgIcon} />

you may write assertion like

expect(imgElementYouMayFind.props.src)
  .toEqual('moon.svg')