My 2000 S-10 Chevy Blazer is overheating. I took the radiator cap off and don't see the water flooding through.

check coolant level - radiator cap - stat operation -water pump --and the electronic clutch for fan vehicle overheating

I put water/coolant mixture in the radiator in the morning ???? You need to do this every morning ? Radiator cap . Have it tested along with the cooling system , pressure tested . Cooling fans work ? White somke coming from the tail pipe , coolant in the oil ?

First, see if the radiator fans are running properly and the water pump belt is on correctly and there's no play in the water pump pulley. Check the front of the radiator fins for clogging. Then check the operation of the thermostat. If those check out, perform a cooling system pressure test on the system and the radiator cap.

Physically look in the radiator under the cap(if one exsist's) when cool, for coolant level, and check the valve in the cap for sticking. If air is present in the radiator it can't get out, and more coolant can't get in,(from the overflow). Either clean the cap or replace it and check that it is the CORRECT cap.

If radiator is low on coolant fill it to overflowing, replace cap, and check that coolant overflow is filled to the COLD line or mark. The overflow is normally where you would add coolant. (never overfill the overflow)After refilling as outlined above, check the level every morning for 2 or 3 days until coolant level stops dropping below the cold mark and add coolant to the overflow ONLY. Do not open the radiator cap. Also, if you have even a tiny coolant leak anywhere in the system, air will get drawn in, instead of coolant from the overflow.

For more OVERHEATING PROBLEMS try these...
Radiator fins dirty, clean with a strong stream of water, not high pressure water.
Radiator clogged, try backflushing it, or replace.
Thermostat stuck open or shut, replace it.
Water pump worn out, can no longer move enough coolant, replace it.
Fan shroud broken or missing....
Electric Fan(s) not working, Check the fan, relay, fuse and engine temperature sensor's.
Belt driven fan, belt slipping, fan clutch is bad, fan blades have flattened out.
Air dam under front bumper is gone, loose, or broken. It actually has a purpose other than scraping on the driveway or curbs. It forces air up into and thru the condenser and radiator. If it's loose, airflow can actually push it out of place making it useless or blocking the airflow. Along with that, there may also be a plastic piece attached to the bottom of, and wraps up behind the bumper. If it

how do the fins on the radiator look? straight or bent? is there any leaves or debris caught between the a/c condenser and the radiator? do you have an electric fan or a belt driven fan? does it seem to operate properly?

drain the water don't use it again, Put an ordinary water and warm up the engine. Do this several times and keep observing the water on the radiator with an open cap. Use water flushing if available.. on final stage use coolant mix to radiator water.

take cap off of radiator and crank motor wait for it to get to operational heat and watch in cap to see if thermostat is opening,you will see water circulating threw radiator if this doesnt happen then water pump is not working you might also flush radiator out

If you don't see a cap, you don't have one. If you are flushing in hopes of correcting an overheating problem, be aware that if the radiator is partially obstructed, the flush chems sold today are too mild to actually do much. The better chems were all banned by the epa.
If you are just doing routine maintenance, easiest method of draining is to remove the lower hose at the radiator, let the system drain, put the hose back on, fill with water and any chems you want to use, run it as per instructions, drain again, fill with more water and repeat with water at least twice before draining and filling with new antifreeze.(do all flushing with heater on full heat) Keep the cap off while doing this so you don't build up pressure and be careful draining hot water. Even though they are mild for the job, chems can still irritate your skin so be careful. When filling for the final time, make sure the system is full and the thermostat has opened before closing it up. Always check everything over for leaks.Any other questions? Just ask!!

The only thing missing from your narration is the water pump. Check to make sure that you are not losing coolant from the water pump. Make sure it is not leaking coolant. If there is evidence of leaking, the water pump is bad. You must take extreme caution when dealing with the cooling system (hot liquid under pressure; not a pleasant thought), but you can remove the radiator cap and start the engine. Check the coolant in the radiator for movement/circulation. If the water pump is functioning properly, there should be some visible sign of water/coolant circulation. The water pump may not be at fault, but with the other upgrades you made to the cooling system, some gunk (for lack of a better word) may have broken loose and clogged the ports in the water hose. You can also remove the hose at the water pump and check for anything clogging up the works. Really sorry for your trouble and I hope this helped. Best wishes.

open the drain valve on the bottom inside of the radiator, run the engine with the garden hose in the radiator cap, have the heater switched on high temp.  After the water comes out clean, turn off engine and let all water drain out.  Replace with 50/50 mix if distilled water and antifreeze.  Collect old antifreeze as it is very toxic and poisonous.