The below code will do so
Public Sub DeleteFromBlob(filename As String, connectionString As String, containerName As String)
' Retrieve storage account from connection string.
Dim storageAccount As CloudStorageAccount = CloudStorageAccount.Parse(connectionString)
' Create the blob client.
Dim blobClient As CloudBlobClient = storageAccount.CreateCloudBlobClient()
' Retrieve reference to a previously created container.
Dim container As CloudBlobContainer = blobClient.GetContainerReference(containerName)
' Retrieve reference to a blob named "myblob.csv".
Dim blockBlob As CloudBlockBlob = container.GetBlockBlobReference(filename)
' Delete the blob.
blockBlob.Delete()
End Sub