The update query is not working.
The problem is that the value of $rs->TestAssignmentId, $currecord, is not passed to the if block. 
This should happen when user presses the submit button.
$sql="SELECT * FROM tbltestassignment
    WHERE TeacherId=".$_SESSION["UserId"]." AND StudentId=".$_GET["StudentId"]." AND TestId=".$_GET["TestId"];
$searchRes1 = Execute($sql);
while($rs=mysql_fetch_object($searchRes1)) {
    $temp = GetSingleReconrd('tbltestassignment','QuestionIds','StudentId',$rs->StudentId);
    $quesIds = explode(',',$temp);
    $totalQues = count($quesIds);
    $currecord = $rs->TestAssignmentId;
    $temp = GetSingleReconrd('tbltestassignment','AnswerIds','StudentId',$rs->StudentId);
    $ansIds = explode(',',$temp);
}
    //echo "<pre>".$currecord."</pre>";
if(isset($_REQUEST["epSave"])) {
    $score = array_filter($_REQUEST['score']);
    $sqlup = 'UPDATE tbltestassignment SET `Score` = "'.$score.'" WHERE `TestAssignmentId` = '.$currecord;
    mysql_query($sqlup);
    $_SESSION["_msg"] = "Marks Successfully Added..!";
    $_SESSION["_msgtype"] = 1;
    $a=8;
    $url = "correct.php?TestId=".$a;//$_GET['TestId'];
    header("location:".$url);
    die();
}
<?php
    for($i=0; $i<$totalQues; $i++){
?>
<tr>
    <td style="text-align:center">
        <input name="score[]" id="score<?php echo $i ?>" type="text" placeholder="Enter marks here">
    </td>
</tr><?php } ?>
 
     
    