First, read this for future reference so we can read your code better:
Then, about your problem:
- adda ref to the button
<button ref="theButton" type=“button” data-url-desc=”/category/network-cable-x-10">
- use the ref in the method to access the element
// a method in your component:
const button = this.$refs.theButton
const url = button.dataset.UrlDesc
axios.get(url).then(/* ... */)
I removed all stuff from the button that was not important to the answer.
If you can’t set a ref due to external factors, you will have to select the button with
document.querySelector('[data-id="1078747405"]') or whatever selector is suited best to your situation.