They had to lend France troops which marched with him into Russia.
So did Austria and Prussia.
Napoleon didn't want to waste his own troops to charge against a heavily fortified position of the Russian/Prussian allies.
Napoleon has directed several assaults against the fortified positions at Borodino, with both French and foreign troops. Prussian troops, which were on the French and not on the Russian side, were not present at Borodino, except for some light cavalry under French command. The attack of the cavalry was not ordered until the fortifications were so badly mauled by continuous assaults that cavalry could simply ride over it.
Hence he sent in wave after wave of Saxon cuirassiers
As well as French Cuirassiers and other cavalry. The Saxon regiments got fame for the attack, but they were certainly not the only ones charging.
the saxons got totally beaten up and lost nearly all men
They took serious casualties, even though you do not specify the amount, but you left out the parts where the French (and all troops at Borodino)did too, as well as taking the positions. The attack, however costly, was a success.
The saxons were still in anger of that at the Battle of Nations.
So you are saying the Saxons were very angry at Napoleon, yet stayed trustworthy allies for over a year, while Austria and Prussia abandoned him?