Please check following code I have implemented using PHP.
Use Following code in your index file
$(document).ready(function() {
            Dropzone.autoDiscover = false;
            var fileList = new Array;
            var i =0;
            $("#some-dropzone").dropzone({
                addRemoveLinks: true,
                init: function() {
                    // Hack: Add the dropzone class to the element
                    $(this.element).addClass("dropzone");
                    this.on("success", function(file, serverFileName) {
                        fileList[i] = {"serverFileName" : serverFileName, "fileName" : file.name,"fileId" : i };
                        //console.log(fileList);
                        i++;
                    });
                    this.on("removedfile", function(file) {
                        var rmvFile = "";
                        for(f=0;f<fileList.length;f++){
                            if(fileList[f].fileName == file.name)
                            {
                                rmvFile = fileList[f].serverFileName;
                            }
                        }
                        if (rmvFile){
                            $.ajax({
                                url: "http://localhost/dropzone/sample/delete_temp_files.php",
                                type: "POST",
                                data: { "fileList" : rmvFile }
                            });
                        }
                    });
                },
                url: "http://localhost/dropzone/sample/upload.php"
            });
        });
Upload.php
<?php
$ds = DIRECTORY_SEPARATOR;  // Store directory separator (DIRECTORY_SEPARATOR) to a simple variable. This is just a personal preference as we hate to type long variable name.
$storeFolder = 'uploads';   // Declare a variable for destination folder.
if (!empty($_FILES)) {
    $tempFile = $_FILES['file']['tmp_name'];          // If file is sent to the page, store the file object to a temporary variable.
    $targetPath = dirname( __FILE__ ) . $ds. $storeFolder . $ds;  // Create the absolute path of the destination folder.
    // Adding timestamp with image's name so that files with same name can be uploaded easily.
    $date = new DateTime();
    $newFileName = $date->getTimestamp().$_FILES['file']['name'];
    $targetFile =  $targetPath.$newFileName;  // Create the absolute path of the uploaded file destination.
    move_uploaded_file($tempFile,$targetFile); // Move uploaded file to destination.
    echo $newFileName;
}
?>
delete_temp_files.php
<?php
$ds = DIRECTORY_SEPARATOR;  // Store directory separator (DIRECTORY_SEPARATOR) to a simple variable. This is just a personal preference as we hate to type long variable name.
$storeFolder = 'uploads'; 
$fileList = $_POST['fileList'];
$targetPath = dirname( __FILE__ ) . $ds. $storeFolder . $ds;
if(isset($fileList)){
    unlink($targetPath.$fileList);
}
?>
Hope this will be helpful for uploading images using ajax and delete using ajax :)
I have found from following references:
Dropzone.js- How to delete files from server?
Dropzone.js remove button with php
Also add following code in your dropzone.js file after line #1110 for preventing user to upload duplicate files with same name :)
Dropzone.prototype.addFile = function(file) {
    if (this.files.length) {
        var _i, _len;
        for (_i = 0, _len = this.files.length; _i < _len; _i++) {
            if(this.files[_i].name === file.name && this.files[_i].size === file.size) {
                return false;
        }
    }
}
Reference Link: https://www.bountysource.com/issues/2993843-dropzone-did-not-check-the-duplicate-file-on-addfile?utm_campaign=plugin&utm_content=tracker%2F283989&utm_medium=issues&utm_source=github