Upgrade new bike to 11 speed or downgrade trainers wheel to 8 speed I am farily new to cycling and roadbikes in general. I have bought a ( last years model ) roadbike with an 8 speed casette in the back. I also bought an indoor trainer ( 2nd hand ) and got a spare wheel with special training tyre on it. However, the casette on the spare wheel is an 11 speed. I have tried to fit that wheel on my bike, but the 11 speed does not ride well on my 8 speed bike. I took it off to prevent any possible damage to the bike and or wheels. 

Is it possible for me to simply take out 3 cogs from my 11 speed wheel, and thus make it an 8 speed? If so, how do I determine which ones to take out? 
Or would it be better if I 'downgrade' my spare wheel to an 8 speed? Or upgrade my bike to an 11 speed ( but I think this will be to expensive for me right now )? 

Keep in mind the bike is new, so the 8 speed casette is not even worn out. The 11 speed wheel is used, but looks in very good shape. 
Also my budget is very limited. Thanks for any helpful tips
The spacing/pitch between the individual cogs of the 8 and 11 speed cassettes are different so if you want to make the training bike work properly with the 11spd cassette you will have to replace your right side shifter (shifter for the rear derailleur) with an 11 speed version or with a friction shifter. Also since (as pointed out by @Argenti Apparatus) the actuation ratio of 8 and 11 speed derailleurs are different, you will need to replace the derailleur with an 11 speed compatible derailleur. Removing a few cogs from the 11 spd cassette won't work due to the different cog spacing as long as you don't upgrade to an 11 SPD shifter due to the different spacing between the cogs. You can ride it but you won't be able to properly index it and the drivetrain will wear out faster and you probably won't be able to shift into some of the gears due to not being able to properly index it.

Do keep in mind 8 speed cassettes are a lot cheaper than 11 speed so the replacement parts (cogs or entire cassette, when the current cassette is worn) will be more expensive also.