You need instead of this code

let output = value - currentTime

use this

let output = value - (currentTime * 1000)

let currentTime = 0;
let intervalClear;
let input = document.getElementById('input');
let button = document.getElementById('button')
button.addEventListener('click', ()=>{
    let value = input.value * 60000;
    function getTime(){
        currentTime++
        function backcount(currentTime){
            let output = value - (currentTime * 1000)
            console.log(output);
            const mint = document.getElementById('mint'),
            sec = document.getElementById('sec');

            let minute = Math.floor(output/60000)
            let second = ((output % 60000) / 1000).toFixed(0)
            mint.innerText = minute;
            sec.innerText = second;

            if(output == 0){
                clearInterval(intervalClear)
            }
        }
        backcount(currentTime);
    }
    getTime()
    intervalClear = setInterval(getTime, 1000)
})

const reset = document.getElementById('reset')
reset.addEventListener('click', ()=>{
    clearInterval(intervalClear);
    input.value = '';
})

<input type="number" id="input" value="" placeholder="Enter time in minutes">
<button id="button">Go</button>
<button id="reset">reset</button>

<div class="timer">
    <div class="mint" id="mint"></div>
    <div class="sec" id="sec"></div>
</div>

Based on @Oleg Barabanov's answer I found one bug. If you didn't enter any value in text box or first added value then click on "Reset" and click on "Go" button then counter started with negative value. I fixed that issue with this code.

Script

    var intervalClear;
    var input = document.querySelector('#input');
    var mint = document.querySelector('#mint');
    var sec = document.querySelector('#sec');
    var go_button = document.querySelector('#button');
    var reset_button = document.querySelector('#reset');

    go_button?.addEventListener('click', () => {
        if (input.value != '' && input.value != 0 && parseInt(input.value) != NaN) {
            startTimer(input.value, mint, sec);
        }
    });

    reset_button?.addEventListener('click', () => {
        clearInterval(intervalClear);
        mint.textContent = '00';
        sec.textContent = '00';
    });

    function startTimer(duration, minElement, secElement) {
        clearInterval(intervalClear);
        var timer = duration * 60, minutes, seconds;
        intervalClear = setInterval(function () {
            minutes = parseInt(timer / 60, 10);
            seconds = parseInt(timer % 60, 10);

            minutes = minutes < 10 ? "0" + minutes : minutes;
            seconds = seconds < 10 ? "0" + seconds : seconds;

            minElement.textContent = minutes;
            secElement.textContent = seconds;

            if (--timer < 0) {
                timer = duration;
            }

            if (minutes == 0 && seconds == 0) {
                clearInterval(intervalClear);
                mint.textContent = '00';
                sec.textContent = '00';
            }
        }, 1000);
    }

DOM

    <input type="number" id="input" placeholder="Enter time in minutes" >
    <button id="button">Go</button>
    <button id="reset">reset</button>

    <div class="timer">
      <div class="mint" id="mint">00</div>
      <div class="sec" id="sec">00</div>
    </div>