Would they reduce by a significant amount? No, but that is not the question asked. In fact, it may make criminals more violent and daring to escape, since the punishments are more harsh (i.E. Nothing to lose), but overall I would be very surprised crime would not go down by some degree.
Now days theft and crime is one of the easiest things to do. People are undergoing more and more threat and eventually people wont be able to go outside with out being robed at least twice. The punishment need to harsher because not inly are you robing some one but they need that money to eat and live and its not ok.
Chopping off a hand for the punishment of theft may sound like a medieval punishment to people of today, as a society we have forgot how harmful the crime of theft is to businessmen/women. Their businesses are their livelihoods it is how they feed their families and pay their bills. It is wrong that many people today can steal whatever they want, receive a small slap on the wrist and go back to stealing again. Theft is an immoral sin which has not been stamped out, the criminals no longer fear punishment, a hand chop as barbaric as it sounds would make thieves think twice about risking their limb. In some cases if the theft was out of genuine hunger then the perp can be sympathised with, but most steal out of greed and arrogance.
While the idea that harsher penalties will deter crimes is an appealing concept, one that many tout as simply making sense intuitively, the reality of the issue is far different. There must be punishments in order to deter crime, but the severity matters far less than the certainty of them being imposed.
It would be reasonable to group those committing crimes into three categories: those that believe they will be caught, those who believe they will not be caught, and those whom don't consider the consequences (crime of passion, etc).
For those that believe they will be caught, the severity does matter. However, the severity of the punishment also influences the severity of their crime. If someone in poverty needing food knew they would be put in jail for a few days for stealing a few food items, they might be willing to accept that in exchange for the food. If they knew they would have their hands cut off for stealing a few food items, and were resolved to steal anyways, why wouldn't they escalate their crime? If the end result is going to be death or a consequence roughly equivalent to ensuring their death, they have no reason not to do more for themselves at the expense of others. Stealing as much as they can and trying to flee, possibly killing people in the process, has the same end consequence in their mind as stealing a small amount and giving themselves up.
For those that believe they will not be caught, the severity of punishment matters far less than the certainty of it. The gamble in their minds is an all-or-nothing venture; they are either caught, or they are not caught, and they are betting on the latter. Regardless of the harshness of the punishment (within reason - not talking about slaps on the wrist for murder), they will treat being punished at all as a loss.
For those that do not think about the consequences, while neither the severity nor the certainty will be all that effective as deterrents, the certainty of punishment would be more likely to make dealing with the aftermath easier. An extremely harsh punishment would back them into a corner and prompt gambling on not being caught, whereas an extremely certain, but moderated, punishment would instead prompt cooperating in hopes of reducing the severity further. After all, if it's already certain that they're going to be caught and cooperation will result in a less severe punishment, why not go with that option?
''Increasing the risk of arrest and the likelihood of going to prison produces modest reductions in property and violent crime,'' Dr Weatherburn said. ''But increasing the length of prison sentences exerts no effect at all.''
If we were willing to apply extreme punishments as a norm, i.e. death for all serious crimes, rigorous imprisonment for intermediate offences and harsh floggings for most other offences, we would almost certainly see a reduction in crime. However, even in the harshest regimes people still continue to commit crimes, so it is clear that a reduction is the best we can hope for. But how many of us would wish to live in such a society? This sort of punitive regime is, therefore, very unlikely to occur within a Western democracy because people do not want it and would not vote for it.
If the punishment for theft is amputation, regardless of whether an object stolen is worth a penny or a gold coin, then the thief would have more of an incentive to go for the gold coin.
In addition, theft in itself has many different variations. Should information thieves like bank fraud or hackers have their hands cut off? Should book plagiarists also suffer this fate?
Life is not black and white, judgement's have to be malleable to accommodate the situation.