SIR—I have the honor to inform you that the expedition sent up the Yazoo river the day after I took possession of the forts on Snyder’s Bluff, has returned, having met with perfect success. As the steamers approached Yazoo city the rebel property was fired by Lieutenant Brown, of the ram Arkansas; and what he began our forces finished. Three powerful rams were burned, the Mobile, a screw vessel, ready for plating; the Republic, being fitted for a ram, with railroad iron plating, and a vessel on the stocks—a monster, three hundred and ten feet long and seventy-five feet beam. This vessel was to have been covered with four and a half inch iron plating, and was to have had six engines, four side wheels and propellers. She would have given us much trouble. The rebels had under construction a fine navy yard, containing fine sawing and planing machines, and an extensive machine shop, carpenter and blacksmiths’ shops, and all the necessary appliances for a large building and repairing yard. Lieutenant-Commander Walker burned all these, with a large quantity of valuable building timber. He also burned a large saw mill that had been used in constructing the monster ram. The material destroyed, at a moderate estimate, would cost more than two millions of dollars. We had one man killed and seven wounded by field pieces from the enemy’s batteries going up the river, but the wounded are doing well. I enclose Lieutenant-Commander Walker’s report in relation to this affair. He deserves much credit for the handsome manner in which he performed the duty assigned him. If he could have obtained pilots he would have succeeded in getting possession of all the rebel rams, instead of having them burned. I am, very respectfully, your obedient servant. DAVID D. PORTER, Acting Rear-Admiral, Commanding Mississippi Squadron. HON. GIDEON WELLES, Secretary of the Navy. From the 22d of May, until the 25th of June, no attempt was made to take the city by direct assault. During all that time, however, the mining operations had been carried on successfully, and on the latter day a fort on the immediate right of the Jackson road was blown up. It was occupied by the Third Louisiana regiment, but the troops had been withdrawn, and only a few were wounded by the explosion. An advance by a small portion of the Federal force, immediately after, was the occasion of a bloody contest, in which the Unionists were defeated, and compelled to retire.