There is no way to to make all code synchronous, you can use callbacks or promises/await to wait for the response. 
Example with callback:
{
            send: function (e) {
                e.preventDefault();
                var self = this;
                var is_submit = self.$target.find('#is_submit').val();
                var mobile = self.$target.find('#mobile').val();
                var phone = self.$target.find('#phone').val();
                var data = self.ajaxcall(mobile, function(result){
                    console.log('the result is: ', result)
                    self._super(e);
                });
            },
            ajaxcall: function (mobile, callback) {
                var value = {
                    'flag': 'mobile',
                    'number': mobile
                }
                ajax.jsonRpc('/checkexisting/', 'call', value).then(function (data) {
                    console.log('isnide ajax call', data);
                    callback(data);
                });
            }
Example with promises:
{
            send: function (e) {
                e.preventDefault();
                var self = this;
                var is_submit = self.$target.find('#is_submit').val();
                var mobile = self.$target.find('#mobile').val();
                var phone = self.$target.find('#phone').val();
                var data = self.ajaxcall(mobile).then(function(result){
                    console.log('the result is: ', result)
                    self._super(e);
                });
            },
            ajaxcall: function (mobile) {
                var value = {
                    'flag': 'mobile',
                    'number': mobile
                }
                return new Promise(function(res, rej){
                    ajax.jsonRpc('/checkexisting/', 'call', value).then(function (data) {
                        console.log('isnide ajax call', data);
                        res(data);
                    })
                });
            }
Or with await(note the async and await keywords):
{
            send: async function (e) {
                e.preventDefault();
                var self = this;
                var is_submit = self.$target.find('#is_submit').val();
                var mobile = self.$target.find('#mobile').val();
                var phone = self.$target.find('#phone').val();
                var data = await self.ajaxcall(mobile);
                console.log(data)
                self._super(e);
            },
            ajaxcall: function (mobile) {
                var value = {
                    'flag': 'mobile',
                    'number': mobile
                }
                return new Promise(function(res, rej){
                    ajax.jsonRpc('/checkexisting/', 'call', value).then(function (data) {
                        console.log('isnide ajax call', data);
                        res(data);
                    })
                });
            }