Battle on Mius-front has come to the end with defeat of Germans. Fights have revealed the main problems German troops - lack of tanks and infantry. Break Mius-Front has provided Red army of an opportunity for victories over Ukraine in 1943.
Mius offensive in August, yes. The July offensive was however defeated, with Soviet forces stopped and then rolled back to their startline, the only notable operational victory the Germans achieved in the summer of 1943. But of course, it still fulfilled it's fundamental aim, which as Andreas notes was to divert German forces from the Zitadelle offensive.
Incidentally, T and DR were still heavily involved in the fighting against "Rumyantsev", from mid-august on.
As we know, Zitadelle begun on 5 July, absorbing the efforts of a large proportion of HG Süd's resources. The Mius offensive was begun on the 17th, while Zitadelle was still in progress. By the 18th, they had broken through in the centre of AOK 6's positions, and an afternoon counterattack by 16.Pz.Gren.D. failed to restore the situation, as did a renewed counterattack on the 19th by 23.PzD, which had arrived late on the 18th. 5th Shock Army continued the advance Eastwards on the 20th and 21st, before being stopped and held on the 22nd.
Das Reich and Totenkopf received orders already on the 17th July - the day the Mius offensive started - to prepare for redeployment south. However, the basic decision to cancel Zitadelle appears to have been formed earlier, already on the 13th. In this context it is an issue of considerable importance that the Germans were expecting a Soviet offensive, because to the extent that the Mius operation had any direct impact on the decision to cancel Zitadelle, that impact would have needed to come before the operation actually started. But at any rate, the inception of another major Soviet offensive on the 17th must at the very least have lent increased urgency to the desire to disengage forces from Zitadelle in order to shore up other sectors in the East (as well as to deal with the situation in Italy).
At the Mius, the situation remained one of stalemate until II SS-Panzerkorps (with "Reich", "Totenkopf" and 3.PzD) had completed their redeployment on 27 July and was ready to attack on the 30th. It took the Germans until 1 August to achieve any decisive success, when "Reich" broke through the Soviet center after "Totenkopf" and 3.PzD had failed to make headway egainst the Soviet right flank. "Reich", 16.Pz.Gren.D. and 23.PzD then regained the Western bank of the Mius, splitting the Soviet bulge in two and forcing a general Soviet withdrawal back across the river. By 2 August, the first Mius battle was essentially over, though the full recapture of the West bank was only accomplished by the 10th.
Which was just as well for the Germans, because on 3 August Rumyantsev broke loose to the North. Within a few days, all 3 divisions of II-SS PzK was on its way north, while the Corps HQ was ordered to Italy to join Leibstandarte, with III Panzerkorps assuming command of the divisions. They were assembling in the Kharkov area on 5 August, and were first in action on the 6th, though elements were continuing to arrive by rail over the following days. The Corps formed the nucleus of the German side in what may be considered the centrepiece of Rumyantsev, ie the fighting in around Bogodukhov during which the Germans attempted to cut off the Soviet spearheads by a counterthrust from the South. By the end of the month, the Germans had conceded defeat at Kharkov and was in retreat to the Dnepr.
On the 18th, while the Bogodukhov battle was at its height, the second Mius offensive was begun. It quickly achieved important breakthroughs, and this time there were no German reserves at hand with which the offensive could be quickly contained. By the end of August, AOK 6 was in an untenable position, and with the permission to retreat coming far too late, it resulted not only in the loss of the Mius line but also in AOK 6 being quite badly gutted as a force.
So, how important were the Mius offensives? If we accept that the decision to cancel Zitadelle was fundamentally made by the 13th of July (when Hitler informed Manstein of his intention to do just that), then there are obviously limits to the importance that can be ascribed to it in effecting that decision, as the offensive did not actually begin in earnest until the 17th. Also, given that it had essentially run its course when Rumyantsev begun, it did not prevent the Germans from shifting the forces that had ensured victory on the Mius northwards to counter Rumyantsev. But I think it seems probable that the expectation of a Mius offensive played some part in the initial decision to cancel Zitadelle, and also that its actual outbreak played an important role in the abrupt termination of it on the 17th. Furthermore, while the three Panzer Divisions were able to shift quickly north to engage Rumyantsev, they had suffered very serious losses during the Mius fighting, and were as a consequence considerably weakened. Except for the ten-day period during which they disengaged from the Prokhorovka sector and moved to the Mius, they had been in more or less continuous action since 5 July.