How to delete a file using Application.dataPath ?

You need to tab out of Unity then tab back in for the project folder to refresh. Or refresh the asset database in code:

 // refresh editor view
 #if UNITY_EDITOR
 UnityEditor.AssetDatabase.Refresh();
 #endif

http://docs.unity3d.com/ScriptReference/AssetDatabase.Refresh.html

Also, simply just check the file location with your file explorer to see if the file has been added/removed.

Edit : here is an example script. Create a new scene, attach script to an empty gameObject, and hit play. Editor project window refreshes when a file is created or deleted.

CreateAndDeleteFile.cs

 using UnityEngine;
 using System.Collections;
 using System.IO;
 
 public class CreateAndDeleteFile : MonoBehaviour 
 {
     public string fileName = "ob04";
     public string fileExtension = ".txt";
     
     private string guiMessage = "type in a file name and hit save";
     
     
     void OnGUI() 
     {
         GUI.Box( new Rect( 160, 20, 400, 25 ), guiMessage );
         
         fileName = GUI.TextField( new Rect( 20, 20, 120, 25 ), fileName );
         
         if ( GUI.Button( new Rect ( 20, 60, 100, 30 ), "LOAD" ) )
         {
             LoadFile();
         }
         
         if ( GUI.Button( new Rect ( 20, 100, 100, 30 ), "SAVE" ) )
         {
             SaveFile();
         }
         
         if ( GUI.Button( new Rect ( 20, 140, 100, 30 ), "DELETE" ) )
         {
             DeleteFile();
         }
     }
     
     
     void LoadFile() 
     {
         string filePath = Application.dataPath + "/" + fileName + fileExtension;
         
         // check if file exists
         if ( !File.Exists( filePath ) )
         {
             guiMessage = "no " + fileName + " file exists"; //Debug.Log( "no " + fileName + " file exists" );
         }
         else
         {
             guiMessage = fileName + " file exists, reading..."; //Debug.Log( fileName + " file exists, reading ..." );
             
             // read file
             StreamReader readFile = new StreamReader( filePath );
             string readString = readFile.ReadToEnd(); //Debug.Log( readFile.ReadToEnd() );
             readFile.Close();
             
             guiMessage = guiMessage + " : " + readString;
         }
     }
     
     
     void SaveFile() 
     {
         string filePath = Application.dataPath + "/" + fileName + fileExtension;
         
         // check if file exists
         if ( !File.Exists( filePath ) )
         {
             guiMessage = "no " + fileName + " file exists, creating..."; //Debug.Log( "no " + fileName + " file exists, creating..." );
             
             // create new file
             StreamWriter newFile = new StreamWriter( filePath );
             newFile.WriteLine( "Hello, I am a text file :)" );
             newFile.Close();
             
             RefreshEditorProjectWindow();
         }
         else
         {
             guiMessage = fileName + " file already exists"; //Debug.Log( fileName + " file already exists" );
         }
     }
     
     
     void DeleteFile() 
     {
         string filePath = Application.dataPath + "/" + fileName + fileExtension;
         
         // check if file exists
         if ( !File.Exists( filePath ) )
         {
             guiMessage = "no " + fileName + " file exists"; //Debug.Log( "no " + fileName + " file exists" );
         }
         else
         {
             guiMessage = fileName + " file exists, deleting..."; //Debug.Log( fileName + " file exists, deleting..." );
             
             File.Delete( filePath );
             
             RefreshEditorProjectWindow();
         }
     }
     
     
     void RefreshEditorProjectWindow() 
     {
         #if UNITY_EDITOR
         UnityEditor.AssetDatabase.Refresh();
         #endif
     }
 }