I have a mauser 7mm, shoots great. I want to add scope and a new stock. What happens if the barrel is shortened? the gun shoots great now, but has open sites. CAN THE BARREL BE CUT,AND STILL SHOOT THE SAME.

Not to rain on your parade...but it sounds like you have a good shooting full military rifle and want to invest in sporterizing it...do not open this black hole can or worms.

Before you even consider it please go talk to a competent gunsmith...one who does more than just mount scopes...that can give a you a good honest cost estimate of the conversion. Once upon a time back in the early 50's and 60's it was still cheap enough to do full conversions...but not any more.
Take the 3-5-900+ bux and go buy an off the shelf something and save your self a ton of frustration and disappointment...but Yes you can have someone shorten and re crown the barrel for about $75-$150 and it starts there. To bend the bolt to allow for scope use requires a new safety at $? and bolt handle to the tune of ???? plus laborat $40+ an hour...a new unfinished and 95% completed uncheckered stock costs $50 to $1000 from Richards depending on wood quality plus 4-5 hours labor at $40-$50 an hour for the gunsmith...or $100-$125 for a standard style laminate that will still need to be bedded and yadda yadda yadda an you still got to do the trigger yet but you can get a Canjar, Timney or Brownell's for about $75-$130 plus labor to install...or you can save money and time by buying a new off the shelf Rem'Chester something for as little as $350 in a Savage that will shoot better than 90% of the new rifles on the market. JMHO 'cause I've been there too many times to think about it ever again.

Enjoy shooting the old timer as it is and leave it alone.
Ron