As @Sandip Nirmal suggested I’ve used downloadjs and that worked out pretty good! Had to make a few adjustments to my code but in the end it worked out.
My new code
// npm i downloadjs
import download from 'downloadjs'
// method
downloadFile(file) {
const specificationId = this.$route.params.specificationId;
axios
.get(`${this.$API_URL}/api/v1/suppliersmanagement/product-specifications/${specificationId}/fileupload/${file.id}/download`, {
headers: this.headers,
responseType: 'blob', // had to add this one here
})
.then(response => {
const content = response.headers['content-type'];
download(response.data, file.file_name, content)
})
.catch(error => console.log(error));
},