<svg id="illustration"
     width="100" height="100" viewBox="0 0 100 100"
     xmlns="http://www.w3.org/2000/svg">
    <rect width="100" height="100" fill="#f1f3f5"/>
    <circle cx="32" cy="32" r="27" fill="#868e96"/>
    <circle cx="81" cy="44" r="15" fill="#343a40"/>
    <circle cx="55" cy="78" r="19" fill="#495057"/>
</svg>

<p>
    <a href="#" class="link-download">Download displayed SVG</a>
</p>

document.querySelector(".link-download").addEventListener("click", (evt) => {
    const svgContent = document.getElementById("illustration").outerHTML,
          blob = new Blob([svgContent], {
              type: "image/svg+xml"
          }),
          url = window.URL.createObjectURL(blob),
          link = evt.target;

    link.target = "_blank";
    link.download = "Illustration.svg";
    link.href = url;
});