This paper examines how climate policy impacts wood use, the allocation of side streams between energy production and higher-value biochemical products, and greenhouse gas (GHG) emissions in forest bioeconomy. The starting point is the European Union's (EU) climate policy, where burning wood-based side streams for energy is treated as carbon-neutral because emissions from harvesting are calculated in the land-use sector. This policy is compared to an alternative wherein wood use or burning wood-based side streams is taxed according to their carbon dioxide (CO2) content. Numerical analysis shows that by increasing the price of electricity, EU's climate policy with emissions trading favors burning wood-based side streams for energy and reduces cascading use of side streams in the modern pulp mill. For traditional pulp mill using fossil fuels, use of fossil fuels and emissions decrease but other impacts depend on the pass-through rate of allowance price on electricity price. An alternative policy, emissions trading with a carbon tax on burned side stream favors cascading use of side streams for both traditional and modern pulp mills. If the alternative policy consists of emissions trading and a carbon tax on wood use, it dramatically decreases wood and energy use, renewable energy and pulp production and profits for both types of pulp mills. Our results show that there are climate and energy policy instruments targeting forest industry that at the same time might reduce GHG emissions and promote the cascading use of wood-based side streams in pulp mills.