You are referring to the battle of Borodino, which was actually at the tail end of Kutuzov's distinguished career. In fact, he was brought out of retirement to lead the Russian army during Napoleon's invasion. For his other successes, see for example, his campaigns against the Ottomans 1806-1812. In the Battle of the Danube, Kutuzov decisively defeated a much larger Ottoman force. Earlier, he served under Suvorov, another great Russian general, who recognized Kutuzov's ability.

The biggest blemish on Kutuzov's record is the famous Battle of Austerlitz. However the battle was fought against his better judgement and at the insistence of Tsar Alexander.

As far as Napoleon's invasion of Russia, Borodino was only a single battle. One needs to look at the entire campaign in order to draw conclusions. And in the context of that campaign, the fact that Napoleon wasn't able to win decisively at Borodino really meant a strategic defeat. It was understood that the Russian army was weaker so a draw was a perfectly acceptable outcome from the Russian perspective.

After the battle, Kutuzov made a controversial and ultimately brilliant decision to surrender Moscow and to not put his army at risk. He knew that Napoleon's position in Moscow was untenable. At the end of the day, Kutozov did what no other general was able to do, which is force Napoleon into humilitating retreat which reduced his 600,000 strong Grand Armee into a pitiful group of stragglers who barely made it out of Russia.

I would argue with /u/MrMarbles2000 and say that Kutuzov wasn't that great of a general. Besides Austerlitz, Kutuzov wasn't as involved in the Russian front against Napoleon as he was shuttered off to the Russo-Turkish War happening at the same time. The real quality commander of the wars was Bagration, which he showed off his skill at Eylau.

I would attribute Kutuzov's success at Borodino as a failure of Napoleon rather than to the skill of Kutuzov. Rather than use his Guard, Napoleon let his army become exhausted claiming the redoubt. Further, the best time that the Russian army had a chance to properly destroy the French army, at the Battle of Krasnoi because Kutuzov gave a pause and let the French army retreat further. So, I'd give him an acceptable pass because he was able to orchestrate the Russian counter attack on the strategic level but wasn't fully effective at the tactical level.

During Napoleon's Russian campaign? I'd say his former reputation as a general suffered massively.

He took over as commander of the Russian armies from Barclay de Tolly, who had to be relieved after constant retreats from the vastly superior Grande Armeé from the Prussian border all the way back into the Russian heartland and the fall of the holy city of Smolensk, which put Tsar Alexander under massive public and military pressure, not the least from his own brother Konstantin who was commanding a part of the forces.

When Kutusov arrived in the Russian camp he did so under great cheers from the lower ranks, who loved his charming and caring persona and called him "Батюшка" (batyushka, diminutive of "father"). The officers on the other hand were absolutely not amused. Many believed that because of his advanced age of 65 he wasn't fit for the post anymore and Kutusow's inclination towards comfort didn't help the picture either. Even his supporters agreed that his age and gout made him incredibly slow at the quill.
Bagration, commander of the Second Army, wrote to the Tsar that replacing Barclay with Kutusov was "like replacing a priest with a deacon" and the Tsar himself had forced Kutusov to take the accomplished General Benningsen as his chief of staff because he wasn't sure whether the new commander could still handle it.

As a general, Kutusov was very... impractical. He frequently chose to ignore the chain of command and give his orders to anyone at hand, so it would happen that a commander prepared his forces for battle only to find part of it missing because Kutusov had sent it on some other mission behind his back. He also tended to agree to suggestions without considering consequences for his own plan, according to Clausewitz, who was a commander in the Russian Army at that time and present at Borodino.

It didn't help that his chief of staff Benningsen, who was sort of irked by not receiving the command himself, as well as his adjutants Colonel Kajsarov and his son-in-law Kardashev all frequently went over his head and gave their own commands in his name. Barclay, who still served as commander of the First Army since his request for release was denied by the Tsar, commented that "Count Kutusov was merely a pseudonym under which all his staff acted".

And from there Kutusov's reputation really went more down than in any other direction. The constant retreats after Borodino and especially the burning of Moscow, while both strategically the right decision in hindsight, lead to massive discontent and desertion amongst the army as well as the general population, despite Kutusov's tendency to claim every minor skirmish won or even drawn as a great personal victory and blame every loss on someone else under him. This self-propaganda would eventually lead to Tsar Alexander distrusting every word of his because for every one of Kutusov's victory letters he got ten letters of complaint from the other generals.
And even during the French retreat he avoided confronting the main army for the longest time and lost several good chances to cut them off and crush them. According to Clausewitz Kutusov's only contribution to the victory was not engaging the French. Which is fair enough, since Napoleon still had his incredible fame as a commander, but the Tsar didn't like that policy of avoidance all too much and would at times bombard him with letters to finally engage the enemy.

When Wilna was back in Russian control the Tsar himself went and visited the city on the 23^rd of December 1812 to celebrate its liberation and to begrudgingly honour the commander in chief to comply with popular demand. Three days after he had a private conversation with Sir Robert Wilson, British liaison officer to Russia, who quotes him as saying that Kutusov didn't do anything he was supposed to and all his successes were pretty much forced upon him but he still was the hero of the Russian nobility. "Which is why [...] I have to award this man with the First Order of St. George and with that defy the purpose of it, since it is the highest honour of the Empire, and was until now the most unblemished."

Unfortunately, I have no idea what Napoleon thought of Kutusov...