To delete an Index, You can edit an existing table's structure using SQLyog's easy to use Table Editor.
To delete an index, select a table from the Object Browser,
1) Click on "Manage Indexes" icon, or
2) Right click on the table(in the Object Browser) and select the menu option "Manage Indexes", or
3) Press F7 key.
This opens up an Alter Table tab with the focus on Indexes sub tab.
To Delete an Index of Table, click on the (-) sign in the toolbar (the delete button) to delete the selected index(s). Click on Yes to drop the index(s) as shown below.