One of the most effective anti-mine weapon is the M58 MICLIC.
M58 MICLIC - Wikipedia
I know the US gave some to Ukraine, but they probably don't have enough. Nobody ever anticipated encountering mine fields this large or this dense.
The MICLIC also operates best in an environment where it isn't going to encounter enemy artillery or enemy air power. The Ukrainians have done a pretty good job taking out artillery to a point some Russian mil bloggers are getting worried Russia is going to run out of gun tubes. But Russian air is still out there. Hopefully the Ukrainian MICLICs have some friendly AD systems covering them.
One of the lessons of this war is in the modern battlefield environment it's very difficult to take ground when you don't have air superiority. Except for Russia's sprint in the opening days of the war and the Ukrainian break out last September, this war has been very slow slog on all fronts.
We'll see what happens once Ukraine breaches the first line of defense completely. I've seen a lot of evidence that instead of holding back reserves, the Russians pumped everyone into the front line and once the Ukrainians are past them, it could be clear running.
My partner was reading something Dmitri posted from a Russian officer in Donesk. He said the Russians moved a huge number of troops into the region, but instead of setting up a layered defense and rotating troops in and out of the front line so they could rest and refit (which the Ukrainians do), they just threw everyone into the first trenchline which overfilled the trenches and led to a lot of casualties. Especially now that the Ukrainians are using more cluster munitions.
I haven't read anything specific that they were doing anything similar in the south, but the Ukrainians were encountering a lot of forces that I would think would be held in reserve when conducting a defensive operation.
I think Putin issues a stand fast order, which is an order to not give up an inch of territory. It forces commanders to feed all their reserves into trying to hold a position that becomes more and more tenuous. When such an order is given, an army will hold the position unusually well for a while, but when the dam breaks, the enemy is off to the races until the next line of defense can be organized. If the enemy is moving too fast, prepared, but unmanned defensive lines may be of little use because those get overrun before the troops can fill them.