Sounds to me like you have 'water shoots' or epicormic growth. Often when you prune a tree heavily it responds by putting on lots of growth. To avoid this you should never remove more than 1/3 (Please for your trees sake cut less off!) of the branches. Acer palmatum `Bloodgood’ like all maples has actively flowing sap in the spring therefore it is best not to prune them in the fall, winter or early spring as they will not have an opportunity to callus (form wound tissue) before the sap starts to rise. I would recommend pruning in the early fall or late summer. I would also make sure that it is not during a drought.
This being said, the reason the growth was straight up was because of the method you used to prune and not the season. I often prune things at non-textbook times but the secret is to make sure you do it well.
So: How to Prune. I think of pruning as an art and everyone has their own techniques. Yet there are some key principles to follow. 1. Make sure you take no more then 1/3 the material off the specimen. 2. Look at the plant, for how to prune, take advice from its growth habit and make it look natural 3. Leave the branch collar intact, this will allow for better callus development. 4. Start by cutting out inward growth and crossing branches. 5. After this stand back and take a look, have a cup of tea if you have too. This break may stop you from over-pruning; it is like a ‘sober second thought’. 6. Bring back any material to a bud that faces to the outside of the plant. You need to visualize where that bud will go when it is a branch. Try and make sure it fills in any gaps.
If you feel you need to take more then 1/3 of the plant off conduct your pruning over 2 or three years. Just remember the best pruning jobs look like very little has been done, even if it took you all day.
How to Fix your Epicormic Growth Problem well, I don’t know if you can, you have effectively created a pollard out of your small tree. If you want to try to repair the damage start by removing only very few of the worst upwards growths each season. Chopping them all off will only result in the same thing but worse. FYI though, the technique of pollarding was used in Europe for firewood and basket weaving production. They would encourage this growth as it created a new crop every so many years without replanting.