You can call button action as we did on odoo backend using its name on website pages, you need to trigger the function from front page to the model, like:-

odoo.define('module.custom_name', function (require) {
"use strict";
var ajax = require('web.ajax');
var core = require('web.core');
var session = require('web.session');
var base = require('web_editor.base');
var _t = core._t;
base.url_translations = '/website/translations';
var _t = core._t;
var Model = require('web.DataModel');
$(document).ready(function(){
    var model = new Model('Your.Model');
    $('#send_mail_function').click(function(){

        model.call('send_mail_function',[])

    })
});
});