What do you now have to mow this acreage with? It isn't the size of the mower but a pasture allowed to get too tall to mow with a mower will surely stress any mower. Good luck finding a riding lawn mower that will be able to be raised to cut that high. There are however 'brush' mowers...talk about that in a moment.
Pasture grass needs to be cut at least twice per season by a LINE TRIMMER. They have these as self propelled 'brush' mowers You'll be able to blast through tall grass, no bagging, small shrubs. Two acres is a lot to do via hand held line timer but same idea. Hiring someone to do this just might be your best bet. I hired two old guys with two of these machines for one hour. Cost $50 bucks. They did about two acres. These machines are sometimes called Field and Brush mowers. Gnarly and productive.
The more often you mow, keeping the grass as high as possible will keep that pasture healthier. Grass growth slows way down at a higher height. Easier to mow. Do not go below 4 to 6" using a line trimmer or brush mower. Too short of grass will stress your grass and encourage competition by weeds you do not want. If there is a lot of debris left, I'd use a gas blower to blow into piles, rake and remove to compost.
Pasture grass needs fertilizer at least twice per season. Leaving clippings does not replenish chemicals grass needs to be productive and vigorous. Do you have animals grazing on this pasture? Make sure to remove the animals way before they've 'mowed' your grass. They will eat it down so far that your grass crop will be compromised and killed in spots. Remove poop to compost.
To look like a lawn and be able to use your lawn mower, mow once per week, no lower than 3". Fertilize at least twice. Aerate at least once per year. Core aerate and leave cores right where they land. This way you'll be able to use your riding mower. Do not allow more than a week of growth or you will be stressing your mower. Clippings should go into a compost pile or where you want to smother weeds. Not too thick or you'll get smelly goo.
I am a firm believer in gas powered lawn mowers, weed wackers and blowers. 2 acres takes work and electric machines are WHIMPS. I did this for a living for decades, I will never purchase electric anything for the landscape. Use only gasoline with no ethanol. Keep filters replaced, measure oil to mix in gas can, do not just dump. Keep dirt out of these machines and they will last forever. It is also more PRODUCTIVE using gas powered and maybe more FUN? Makes your job easier and you'll be more likely to get out there more often. Wear eye protection and ear protection!
